메뉴 건너뛰기




Volumn 49, Issue 2, 2012, Pages 237-323

Grothendieck's theorem, past and present

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84863088485     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-2011-01348-9     Document Type: Article
Times cited : (207)

References (163)
  • 1
    • 33745038738 scopus 로고    scopus 로고
    • Grothendieck's constant and local models for noisy entangled quantum states
    • 062105
    • A. Acín, N. Gisin and B. Toner, Grothendieck's constant and local models for noisy entangled quantum states, Phys. Rev. A (3) 73 (2006), no. 6, part A, 062105, 5 pp.
    • (2006) Phys. Rev. A (3) , vol.73 , Issue.6 PART A , pp. 5
    • Acín, A.1    Gisin, N.2    Toner, B.3
  • 2
    • 0035981381 scopus 로고    scopus 로고
    • Hankel and Toeplitz-Schur multipliers
    • A.B. Aleksandrov and V.V. Peller, Hankel and Toeplitz-Schur multipliers, Math. Ann. 324 (2002), 277-327.
    • (2002) Math. Ann. , vol.324 , pp. 277-327
    • Aleksandrov, A.B.1    Peller, V.V.2
  • 3
    • 41149128402 scopus 로고    scopus 로고
    • The Grothendieck constant of random and pseudo-random graphs
    • N. Alon and E. Berger, The Grothendieck constant of random and pseudo-random graphs, Discrete Optim. 5 (2008), no. 2, 323-327.
    • (2008) Discrete Optim , vol.5 , Issue.2 , pp. 323-327
    • Alon, N.1    Berger, E.2
  • 5
    • 33747188137 scopus 로고    scopus 로고
    • Approximating the cut-norm via Grothendieck's inequality
    • (electronic)
    • N. Alon and A. Naor, Approximating the cut-norm via Grothendieck's inequality, SIAM J. Comput. 35 (2006), no. 4, 787-803 (electronic).
    • (2006) SIAM J. Comput. , vol.35 , Issue.4 , pp. 787-803
    • Alon, N.1    Naor, A.2
  • 7
    • 65449172136 scopus 로고    scopus 로고
    • Quantum [Un]speakables (Vienna, 2000), 119-153, Springer, Berlin, (arXiv:quant-ph/0402001)
    • A. Aspect, Bell's theorem: the naive view of an experimentalist, Quantum [Un]speakables (Vienna, 2000), 119-153, Springer, Berlin, 2002 (arXiv:quant-ph/0402001).
    • (2002) Bell's theorem: the naive view of an experimentalist
    • Aspect, A.1
  • 8
    • 84863109942 scopus 로고    scopus 로고
    • Quantum Reflections, 69-78, Cambridge Univ. Press, Cambridge
    • A. Aspect, Testing Bell's inequalities, Quantum Reflections, 69-78, Cambridge Univ. Press, Cambridge, 2000.
    • (2000) Testing Bell's inequalities
    • Aspect, A.1
  • 9
    • 42149152090 scopus 로고    scopus 로고
    • Wiley-Vch, VerlagGmbH & Co., KGaA, Weinheim
    • J. Audretsch, Entangled Systems, Wiley-Vch, VerlagGmbH & Co., KGaA, Weinheim, 2007.
    • (2007) Entangled Systems
    • Audretsch, J.1
  • 11
    • 84863099399 scopus 로고
    • A collection of problems on operator algebras
    • Proceedings of the CBMS Regional Conference held at Texas Christian University, Fort Worth, Texas, May 19-26, 1990. Edited by Robert S. Doran. Contemporary Mathematics, 120. American Mathematical Society, Providence, RI
    • D. P. Blecher et al., "A collection of problems on operator algebras", pp. 205-214 in Selfadjoint and nonselfadjoint operator algebras and operator theory, Proceedings of the CBMS Regional Conference held at Texas Christian University, Fort Worth, Texas, May 19-26, 1990. Edited by Robert S. Doran. Contemporary Mathematics, 120. American Mathematical Society, Providence, RI, 1991.
    • (1991) Selfadjoint and nonselfadjoint operator algebras and operator theory , pp. 205-214
    • Blecher, D.P.1
  • 12
    • 84863103838 scopus 로고
    • Tracially completely bounded multilinear maps on C*-algebras
    • D. Blecher, Tracially completely bounded multilinear maps on C*-algebras, J. London Math. Soc. 39 (1989), no. 3, 514-524.
    • (1989) J. London Math. Soc. , vol.39 , Issue.3 , pp. 514-524
    • Blecher, D.1
  • 13
    • 0013076061 scopus 로고
    • Generalizing Grothendieck's program, "Function spaces"
    • K. Jarosz (ed.), Marcel Dekker
    • D. Blecher, Generalizing Grothendieck's program, "Function spaces", K. Jarosz (ed.), Lecture Notes in Pure and Applied Math., Vol. 136, Marcel Dekker, 1992.
    • (1992) Lecture Notes in Pure and Applied Math , vol.136
    • Blecher, D.1
  • 14
    • 33645933545 scopus 로고
    • Multidimensional extensions of the Grothendieck inequality and applications
    • R.C. Blei, Multidimensional extensions of the Grothendieck inequality and applications, Ark. Mat. 17 (1979), 51-68.
    • (1979) Ark. Mat. , vol.17 , pp. 51-68
    • Blei, R.C.1
  • 16
    • 0011052236 scopus 로고
    • Herz-Schur multipliers and completely bounded multipliers of the Fourier algebra of a locally compact group
    • M. Bozejko and G. Fendler, Herz-Schur multipliers and completely bounded multipliers of the Fourier algebra of a locally compact group, Boll. Unione Mat. Ital. (6) 3-A (1984), 297-302.
    • (1984) Boll. Unione Mat. Ital. , vol.3 A , Issue.6 , pp. 297-302
    • Bozejko, M.1    Fendler, G.2
  • 22
    • 42149120579 scopus 로고    scopus 로고
    • Optimal constants in Khintchine type inequalities for Fermions, Rademachers and q-Gaussian operators
    • A. Buchholz, Optimal constants in Khintchine type inequalities for Fermions, Rademachers and q-Gaussian operators, Bull. Polish Acad. Sci. Math. 53 (2005), 315-321.
    • (2005) Bull. Polish Acad. Sci. Math. , vol.53 , pp. 315-321
    • Buchholz, A.1
  • 23
    • 17744363129 scopus 로고    scopus 로고
    • Maximizing quadratic programs: extending Grothendieck's inequality
    • M. Charikar and A. Wirth, Maximizing quadratic programs: extending Grothendieck's inequality, FOCS (2004), 54-60.
    • (2004) FOCS , pp. 54-60
    • Charikar, M.1    Wirth, A.2
  • 24
    • 0001279362 scopus 로고
    • Nuclear C*-algebras and injectivity: the general case
    • M.D. Choi and E. Effros, Nuclear C*-algebras and injectivity: the general case, Indiana Univ. Math. J. 26 (1977), 443-446.
    • (1977) Indiana Univ. Math. J , vol.26 , pp. 443-446
    • Choi, M.D.1    Effros, E.2
  • 25
    • 56749178859 scopus 로고    scopus 로고
    • A linearization of Connes' embedding problem
    • B. Collins and K. Dykema, A linearization of Connes' embedding problem. New York J. Math. 14 (2008), 617-641.
    • (2008) New York J. Math. , vol.14 , pp. 617-641
    • Collins, B.1    Dykema, K.2
  • 26
    • 0002179940 scopus 로고
    • λ, λ ≠ 1
    • λ, λ ≠ 1, Ann. of Math. (2) 104 (1976), 73-115.
    • (1976) Ann. of Math , Issue.2 , pp. 73-115
    • Connes, A.1
  • 28
    • 85013512039 scopus 로고
    • North-Holland Mathematics Studies, 176. North-Holland Publishing Co., Amsterdam
    • A. Defant and K. Floret, Tensor norms and operator ideals, North-Holland Mathematics Studies, 176. North-Holland Publishing Co., Amsterdam, 1993.
    • (1993) Tensor norms and operator ideals
    • Defant, A.1    Floret, K.2
  • 31
    • 0346995375 scopus 로고
    • Les anneaux d'opérateurs de classe finie
    • J. Dixmier, Les anneaux d'opérateurs de classe finie, Ann. Sci. École Norm. Sup. 66 (1949), 209-261.
    • (1949) Ann. Sci. École Norm. Sup. , vol.66 , pp. 209-261
    • Dixmier, J.1
  • 34
    • 0001126252 scopus 로고
    • A new approach to operator spaces
    • E.G. Effros and Z.J. Ruan, A new approach to operator spaces, Canadian Math. Bull. 34 (1991), 329-337.
    • (1991) Canadian Math. Bull. , vol.34 , pp. 329-337
    • Effros, E.G.1    Ruan, Z.J.2
  • 35
    • 0004235090 scopus 로고    scopus 로고
    • The Clarendon Press, Oxford University Press, New York, xvi-363
    • E.G. Effros and Z.J. Ruan, Operator Spaces, The Clarendon Press, Oxford University Press, New York, 2000, xvi+363 pp.
    • (2000) Operator Spaces
    • Effros, E.G.1    Ruan, Z.J.2
  • 36
    • 2542485677 scopus 로고
    • Bell inequalities, Grothendieck's constant, and root two
    • P.C. Fishburn and J.A. Reeds, Bell inequalities, Grothendieck's constant, and root two, SIAM J. Discrete Math. 7 (1994), no. 1, 48-56.
    • (1994) SIAM J. Discrete Math. , vol.7 , Issue.1 , pp. 48-56
    • Fishburn, P.C.1    Reeds, J.A.2
  • 40
    • 84893574327 scopus 로고
    • Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
    • M.X. Goemans and D.P. Williamson, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, J. Assoc. Comput. Mach. 42 (1995), 1115-1145.
    • (1995) J. Assoc. Comput. Mach. , vol.42 , pp. 1115-1145
    • Goemans, M.X.1    Williamson, D.P.2
  • 41
    • 0002975215 scopus 로고
    • Résumé de la théorie métrique des produits tensoriels topologiques
    • São-Paulo1-79. Reprinted in Resenhas 2(4), 1996
    • A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Boll. Soc. Mat. São-Paulo 8 (1953), 1-79. Reprinted in Resenhas 2 (1996), no. 4, 401-480.
    • (1953) Boll. Soc. Mat , vol.8 , pp. 401-480
    • Grothendieck, A.1
  • 42
    • 0011608594 scopus 로고
    • Sur certaines classes de suites dans les espaces de Banach et le théorème de Dvoretzky-Rogers
    • Reprinted in Resenhas 3 4 1998 447-477
    • A. Grothendieck, Sur certaines classes de suites dans les espaces de Banach et le théorème de Dvoretzky-Rogers, Bol. Soc. Mat. São Paulo 8 (1953), 81-110. Reprinted in Resenhas 3 (1998), no. 4, 447-477.
    • (1953) Bol. Soc. Mat. São Paulo. , vol.8 , pp. 81-110
    • Grothendieck, A.1
  • 43
    • 0003244564 scopus 로고
    • Produits tensoriels topologiques et espaces nucléaires (French)
    • 1955
    • A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires (French), Mem. Amer. Math. Soc. 1955 (1955), no. 16, 140 pp.
    • (1955) Mem. Amer. Math. Soc. , Issue.16 , pp. 140
    • Grothendieck, A.1
  • 44
    • 51249185617 scopus 로고
    • The ellipsoid method and its consequences in combinatorial optimization
    • M. Grötschel, L. Lovász and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica 1 (1981), 169-197.
    • (1981) Combinatorica , vol.1 , pp. 169-197
    • Grötschel, M.1    Lovász, L.2    Schrijver, A.3
  • 45
    • 0003207514 scopus 로고
    • Geometric algorithms and combinatorial optimization
    • Second edition, 2 Springer-Verlag, Berlin
    • M. Grötschel, L. Lovász and A. Schrijver, Geometric algorithms and combinatorial optimization, Second edition, Algorithms and Combinatorics, 2, Springer-Verlag, Berlin, 1993.
    • (1993) Algorithms and Combinatorics
    • Grötschel, M.1    Lovász, L.2    Schrijver, A.3
  • 47
    • 0001613468 scopus 로고
    • The best constants in the Khintchine inequality
    • U. Haagerup, The best constants in the Khintchine inequality, Studia Math. 70 (1981), 231-283 (1982).
    • (1982) Studia Math , vol.70 , Issue.1981 , pp. 231-283
    • Haagerup, U.1
  • 48
    • 0000743985 scopus 로고
    • Solution of the similarity problem for cyclic representations of C*-algebras
    • U. Haagerup, Solution of the similarity problem for cyclic representations of C*-algebras, Ann. of Math. (2) 118 (1983), 215-240.
    • (1983) Ann. of Math. (2) , vol.118 , pp. 215-240
    • Haagerup, U.1
  • 49
    • 0000363643 scopus 로고
    • All nuclear C*-algebras are amenable
    • U. Haagerup, All nuclear C*-algebras are amenable, Invent. Math. 74 (1983), no. 2, 305-319.
    • (1983) Invent. Math. , vol.74 , Issue.2 , pp. 305-319
    • Haagerup, U.1
  • 50
    • 46549095811 scopus 로고
    • The Grothendieck inequality for bilinear forms on C*-algebras
    • U. Haagerup, The Grothendieck inequality for bilinear forms on C*-algebras, Adv. Math. 56 (1985), no. 2, 93-116.
    • (1985) Adv. Math , vol.56 , Issue.2 , pp. 93-116
    • Haagerup, U.1
  • 51
    • 51249170925 scopus 로고
    • A new upper bound for the complex Grothendieck constant
    • U. Haagerup, A new upper bound for the complex Grothendieck constant, Israel J. Math. 60 (1987), no. 2, 199-224.
    • (1987) Israel J. Math. , vol.60 , Issue.2 , pp. 199-224
    • Haagerup, U.1
  • 52
    • 0013126091 scopus 로고
    • Grothendieck type norms for bilinear forms on C*-algebras
    • U. Haagerup and T. Itoh, Grothendieck type norms for bilinear forms on C*-algebras, J. Operator Theory 34 (1995), 263-283.
    • (1995) J. Operator Theory , vol.34 , pp. 263-283
    • Haagerup, U.1    Itoh, T.2
  • 53
    • 34547674590 scopus 로고    scopus 로고
    • On the best constants in noncommutative Khintchine-type inequalities
    • U. Haagerup and M. Musat, On the best constants in noncommutative Khintchine-type inequalities, J. Funct. Anal. 250 (2007), 588-624.
    • (2007) J. Funct. Anal. , vol.250 , pp. 588-624
    • Haagerup, U.1    Musat, M.2
  • 54
    • 50249087425 scopus 로고    scopus 로고
    • The Effros-Ruan conjecture for bilinear forms on C*-algebras
    • U. Haagerup and M. Musat, The Effros-Ruan conjecture for bilinear forms on C*-algebras, Invent. Math. 174 (2008), 139-163.
    • (2008) Invent. Math , vol.174 , pp. 139-163
    • Haagerup, U.1    Musat, M.2
  • 55
    • 84973999201 scopus 로고
    • Linear operators between C*-algebras
    • U. Haagerup and G. Pisier, Linear operators between C*-algebras, Duke Math. J. 71 (1993), 889-925.
    • (1993) Duke Math. J. , vol.71 , pp. 889-925
    • Haagerup, U.1    Pisier, G.2
  • 56
    • 0001853393 scopus 로고    scopus 로고
    • Random matrices and K-theory for exact C*-algebras
    • (electronic)
    • U. Haagerup and S. Thorbjørnsen, Random matrices and K-theory for exact C*-algebras, Doc. Math. 4 (1999), 341-450 (electronic).
    • (1999) Doc. Math. , vol.4 , pp. 341-450
    • Haagerup, U.1    Thorbjørnsen, S.2
  • 58
    • 0039833680 scopus 로고    scopus 로고
    • p and non-commutative Λ(p)-sets
    • p and non-commutative Λ(p)-sets, Studia Math. 137 (1999), no. 3, 203-260.
    • (1999) Studia Math , vol.137 , Issue.3 , pp. 203-260
    • Harcharras, A.1
  • 59
    • 0000844603 scopus 로고    scopus 로고
    • Some optimal inapproximability results
    • J. Håstad, Some optimal inapproximability results, J. ACM 48 (2001), 798-859.
    • (2001) J. ACM , vol.48 , pp. 798-859
    • Håstad, J.1
  • 60
    • 33748545909 scopus 로고    scopus 로고
    • Quantum correlation and Grothendieck's constant
    • H. Heydari, Quantum correlation and Grothendieck's constant, J. Phys. A 39 (2006), no. 38, 11869-11875.
    • (2006) J. Phys. A , vol.39 , Issue.38 , pp. 11869-11875
    • Heydari, H.1
  • 61
    • 84972550545 scopus 로고
    • On the convergence of sums of independent Banach space valued random variables
    • K. Itô and M. Nisio, On the convergence of sums of independent Banach space valued random variables, Osaka J. Math. 5 (1968), 35-48.
    • (1968) Osaka J. Math. , vol.5 , pp. 35-48
    • Itô, K.1    Nisio, M.2
  • 62
    • 84863085584 scopus 로고
    • On the completely bounded map of a C*-algebra to its dual space
    • T. Itoh, On the completely bounded map of a C*-algebra to its dual space, Bull. London Math. Soc. 19 (1987), 546-550.
    • (1987) Bull. London Math. Soc. , vol.19 , pp. 546-550
    • Itoh, T.1
  • 63
    • 0011356701 scopus 로고
    • On the compact nonnuclear operator problem
    • K. John, On the compact nonnuclear operator problem, Math. Ann. 287 (1990), 509-514.
    • (1990) Math. Ann. , vol.287 , pp. 509-514
    • John, K.1
  • 65
    • 22344439636 scopus 로고    scopus 로고
    • Embedding of the operator space OH and the logarithmic 'little Grothendieck inequality'
    • M. Junge, Embedding of the operator space OH and the logarithmic 'little Grothendieck inequality', Invent. Math. 161 (2005), no. 2, 225-286.
    • (2005) Invent. Math. , vol.161 , Issue.2 , pp. 225-286
    • Junge, M.1
  • 69
    • 77952089528 scopus 로고    scopus 로고
    • Maurey's factorization theory for operator spaces
    • M. Junge and J. Parcet, Maurey's factorization theory for operator spaces, Math. Ann. 347 (2010), no. 2, 299-338.
    • (2010) Math. Ann. , vol.347 , Issue.2 , pp. 299-338
    • Junge, M.1    Parcet, J.2
  • 71
    • 0001340099 scopus 로고
    • Bilinear forms on exact operator spaces and B(H)⊗B(H)
    • M. Junge and G. Pisier, Bilinear forms on exact operator spaces and B(H)⊗B(H), Geom. Funct. Anal. 5 (1995), no. 2, 329-363.
    • (1995) Geom. Funct. Anal. , vol.5 , Issue.2 , pp. 329-363
    • Junge, M.1    Pisier, G.2
  • 72
    • 77951209048 scopus 로고    scopus 로고
    • Representation of certain homogeneous Hilbertian operator spaces and applications
    • M. Junge, and Q. Xu, Representation of certain homogeneous Hilbertian operator spaces and applications, Invent. Math. 179 (2010), no. 1, 75-118
    • (2010) Invent. Math. , vol.179 , Issue.1 , pp. 75-118
    • Junge, M.1    Xu, Q.2
  • 74
    • 0003851494 scopus 로고
    • Cambridge Studies in Advanced Mathematics, 5 Cambridge University Press, Cambridge
    • J.P. Kahane, Some random series of functions, Second edition, Cambridge Studies in Advanced Mathematics, 5, Cambridge University Press, Cambridge, 1985.
    • (1985) Some random series of functions, Second edition
    • Kahane, J.P.1
  • 75
    • 19444384814 scopus 로고
    • Projective tensor products of C*-algebras
    • S. Kaijser and A.M. Sinclair, Projective tensor products of C*-algebras, Math. Scand. 55 (1984), no. 2, 161-187.
    • (1984) Math. Scand. , vol.55 , Issue.2 , pp. 161-187
    • Kaijser, S.1    Sinclair, A.M.2
  • 76
    • 27844479151 scopus 로고    scopus 로고
    • Rademacher series and decoupling
    • (electronic)
    • N.J. Kalton, Rademacher series and decoupling, New York J. Math. 11 (2005), 563-595 (electronic).
    • (2005) New York J. Math. , vol.11 , pp. 563-595
    • Kalton, N.J.1
  • 77
    • 18444395362 scopus 로고    scopus 로고
    • The Knaster problem and the geometry of high-dimensional cubes
    • B. Kashin and S. Szarek, The Knaster problem and the geometry of high-dimensional cubes, C.R. Math. Acad. Sci. Paris 336 (2003), 931-936.
    • (2003) C. R. Math. Acad. Sci. Paris , vol.336 , pp. 931-936
    • Kashin, B.1    Szarek, S.2
  • 78
    • 30744434916 scopus 로고    scopus 로고
    • On the Gram matrices of systems of uniformly bounded functions (Russian)
    • Funkts. Prostran., Priblizh., Differ.Uravn., 237-243; translation in Proc. Steklov Inst. Math. 227-233, 243, 2003
    • B. Kashin and S. Szarek, On the Gram matrices of systems of uniformly bounded functions (Russian), Tr. Mat. Inst. Steklova 243 (2003), Funkts. Prostran., Priblizh., Differ.Uravn., 237-243; translation in Proc. Steklov Inst. Math. 2003, no. 4 (243), 227-233.
    • (2003) Tr. Mat. Inst. Steklova , vol.243
    • Kashin, B.1    Szarek, S.2
  • 80
    • 77951697840 scopus 로고    scopus 로고
    • Sharp kernel clustering algorithms and their associated Grothendieck inequalities
    • S. Khot and A. Naor, Sharp kernel clustering algorithms and their associated Grothendieck inequalities. In Proceedings of SODA'2010, pp. 664-683.
    • (2010) Proceedings of SODA' , pp. 664-683
    • Khot, S.1    Naor, A.2
  • 82
    • 0000294483 scopus 로고
    • On nonsemisplit extensions, tensor products and exactness of group C*-algebras
    • E. Kirchberg, On nonsemisplit extensions, tensor products and exactness of group C*-algebras, Invent. Math. 112 (1993), 449-489.
    • (1993) Invent. Math. , vol.112 , pp. 449-489
    • Kirchberg, E.1
  • 83
    • 0011022154 scopus 로고
    • Linear and complex analysis problem book
    • Section 6.5, Springer, Berlin
    • S.V. Kislyakov, Linear and complex analysis problem book, Section 6.5, Lecture Notes in Math., 1043, Springer, Berlin, 1984.
    • (1984) Lecture Notes in Math , vol.1043
    • Kislyakov, S.V.1
  • 84
    • 0242610274 scopus 로고
    • Absolutely summing operators on the disc algebra (Russian)
    • translation in St. Petersburg Math. J. 3 1992 705-774
    • S.V. Kislyakov, Absolutely summing operators on the disc algebra (Russian), Algebra i Analiz 3 (1991), no. 4, 1-77; translation in St. Petersburg Math. J. 3 (1992), 705-774.
    • (1991) Algebra i Analiz , vol.3 , Issue.4 , pp. 1-77
    • Kislyakov, S.V.1
  • 85
    • 1842741071 scopus 로고    scopus 로고
    • Banach spaces and classical harmonic analysis
    • North-Holland, Amsterdam
    • S.V. Kislyakov, Banach spaces and classical harmonic analysis, Handbook of the Geometry of Banach Spaces, Vol. I, 871-898, North-Holland, Amsterdam, 2001.
    • (2001) Handbook of the Geometry of Banach Spaces , vol.1 , pp. 871-898
    • Kislyakov, S.V.1
  • 86
    • 84863103265 scopus 로고    scopus 로고
    • On the complex Grothendieck constant in the n-dimensional case
    • London Math. Soc. Lecture Note Ser 158, Cambridge Univ. Press, Cambridge
    • H. König, On the complex Grothendieck constant in the n-dimensional case, Geometry of Banach Spaces (Strobl, 1989), 181-198, London Math. Soc. Lecture Note Ser., 158, Cambridge Univ. Press, Cambridge, 1990.
    • Geometry of Banach Spaces (Strobl, 1989) , vol.158
    • König, H.1
  • 89
  • 90
    • 0041065062 scopus 로고
    • Constantes de Grothendieck et fonctions de type positif sur les sphères
    • J.L. Krivine, Constantes de Grothendieck et fonctions de type positif sur les sph'eres, Adv. in Math. 31 (1979), 16-30.
    • (1979) Adv. in Math. , vol.31 , pp. 16-30
    • Krivine, J.L.1
  • 92
    • 0038609707 scopus 로고    scopus 로고
    • Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI
    • M. Ledoux, The Concentration of Measure Phenomenon, Mathematical Surveys and Monographs, vol. 89, American Mathematical Society, Providence, RI, 2001.
    • (2001) The Concentration of Measure Phenomenon , vol.89
    • Ledoux, M.1
  • 93
    • 51649156232 scopus 로고
    • Factoring operators through Hilbert space
    • D.H. Leung, Factoring operators through Hilbert space, Israel J. Math. 71 (1990), 225-227.
    • (1990) Israel J. Math. , vol.71 , pp. 225-227
    • Leung, D.H.1
  • 96
    • 30744463727 scopus 로고    scopus 로고
    • Semidefinite programs and combinatorial optimization
    • Microsoft Research, Redmont, WA 98052
    • L. Lovász, Semidefinite programs and combinatorial optimization, Lecture Notes, Microsoft Research, Redmont, WA 98052.
    • Lecture Notes
    • Lovász, L.1
  • 98
    • 51249165958 scopus 로고
    • A Grothendieck factorization theorem on 2-convex Schatten spaces
    • F. Lust-Piquard, A Grothendieck factorization theorem on 2-convex Schatten spaces, Israel J. Math. 79 (1992), no. 2-3, 331-365.
    • (1992) Israel J. Math. , vol.79 , Issue.2-3 , pp. 331-365
    • Lust-Piquard, F.1
  • 99
    • 0000426206 scopus 로고
    • Noncommutative Khintchine and Paley inequalities
    • F. Lust-Piquard and G. Pisier, Noncommutative Khintchine and Paley inequalities, Ark. Mat. 29 (1991), no. 2, 241-260.
    • (1991) Ark. Mat. , vol.29 , Issue.2 , pp. 241-260
    • Lust-Piquard, F.1    Pisier, G.2
  • 100
    • 33846838753 scopus 로고    scopus 로고
    • The little Grothendieck theorem and Khintchine inequalities for symmetric spaces of measurable operators
    • F. Lust-Piquard and Q. Xu, The little Grothendieck theorem and Khintchine inequalities for symmetric spaces of measurable operators, J. Funct. Anal. 244 (2007), no. 2, 488-503.
    • (2007) J. Funct. Anal. , vol.244 , Issue.2 , pp. 488-503
    • Lust-Piquard, F.1    Xu, Q.2
  • 101
    • 64549116939 scopus 로고
    • Une nouvelle démonstration d'un théorème de Grothendieck
    • Exp. No. 22 7 pp. Centre de Math., école Polytech., Paris
    • p et applications radonifiantes, Exp. No. 22, 7 pp. Centre de Math., école Polytech., Paris, 1973.
    • (1973) p et applications radonifiantes
    • Maurey, B.1
  • 102
    • 0005345043 scopus 로고
    • p
    • No. 11. Société Mathématique de France, Paris
    • p, Astérisque, No. 11. Société Mathématique de France, Paris, 1974, ii+163 pp.
    • (1974) Astérisque
    • Maurey, B.1
  • 103
    • 17744381831 scopus 로고    scopus 로고
    • Relaxations of quadratic programs in operator theory and system analysis (English summary)
    • Oper. Theory Adv. Appl., 129 Birkhäuser, Basel, 365-392
    • A. Megretski, Relaxations of quadratic programs in operator theory and system analysis (English summary), Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), 365-392, Oper. Theory Adv. Appl., 129, Birkḧauser, Basel, 2001.
    • (2001) Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000)
    • Megretski, A.1
  • 104
    • 0000467513 scopus 로고    scopus 로고
    • On maximization of quadratic form over intersection of ellipsoids with common center
    • A.R.C. Nemirovski and T. Terlaky, On maximization of quadratic form over intersection of ellipsoids with common center, Math. Programming 86 (1999), 463-473.
    • (1999) Math. Programming , vol.86 , pp. 463-473
    • Nemirovski, A.R.C.1    Terlaky, T.2
  • 105
    • 0013127828 scopus 로고    scopus 로고
    • Direct sums of operator spaces
    • T. Oikhberg, Direct sums of operator spaces, J. London Math. Soc. 64 (2001), 144-160.
    • (2001) J. London Math. Soc. , vol.64 , pp. 144-160
    • Oikhberg, T.1
  • 106
    • 22644448910 scopus 로고    scopus 로고
    • The "maximal" tensor product of operator spaces
    • T. Oikhberg and G. Pisier, The "maximal" tensor product of operator spaces, Proc. Edinburgh Math. Soc. 42 (1999), 267-284.
    • (1999) Proc. Edinburgh Math. Soc. , vol.42 , pp. 267-284
    • Oikhberg, T.1    Pisier, G.2
  • 108
    • 7244231166 scopus 로고    scopus 로고
    • About the QWEP conjecture
    • N. Ozawa, About the QWEP conjecture, Internat. J. Math. 15 (2004), no. 5, 501-530.
    • (2004) Internat. J. Math. , vol.15 , Issue.5 , pp. 501-530
    • Ozawa, N.1
  • 109
    • 0026366408 scopus 로고
    • Optimization, approximation, and complexity classes
    • C. Papadimitriou and M. Yannakakis, Optimization, approximation, and complexity classes, J. Comput. System Sci. 43 (1991), 425-440.
    • (1991) J. Comput. System Sci. , vol.43 , pp. 425-440
    • Papadimitriou, C.1    Yannakakis, M.2
  • 111
    • 79951831203 scopus 로고    scopus 로고
    • Representations of logmodular algebras
    • V. Paulsen and M. Raghupathi, Representations of logmodular algebras, Trans. Amer. Math. Soc. 363 (2011), no. 5, 2627-2640.
    • (2011) Trans. Amer. Math. Soc. , vol.363 , Issue.5 , pp. 2627-2640
    • Paulsen, V.1    Raghupathi, M.2
  • 112
    • 0035645328 scopus 로고    scopus 로고
    • Little Grothendieck's theorem for real JB*-triples
    • A. Peralta, Little Grothendieck's theorem for real JB*-triples, Math. Z. 237 (2001), 531-545.
    • (2001) Math. Z , vol.237 , pp. 531-545
    • Peralta, A.1
  • 113
    • 20144379550 scopus 로고    scopus 로고
    • New advances on the Grothendieck's inequality problem for bilinear forms on JB*-triples
    • A. Peralta, New advances on the Grothendieck's inequality problem for bilinear forms on JB*-triples, Math. Inequal. Appl. 8 (2005), 7-21.
    • (2005) Math. Inequal. Appl. , vol.8 , pp. 7-21
    • Peralta, A.1
  • 114
    • 3543090890 scopus 로고
    • Quantum theory: concepts and methods
    • Kluwer Academic Publishers Group, Dordrecht
    • A. Peres, Quantum theory: concepts and methods, Fundamental Theories of Physics, 57, Kluwer Academic Publishers Group, Dordrecht, 1993.
    • (1993) Fundamental Theories of Physics , vol.57
    • Peres, A.1
  • 116
    • 49349121515 scopus 로고
    • Grothendieck's theorem for noncommutative C*-algebras, With an appendix on Grothendieck's constants
    • G. Pisier, Grothendieck's theorem for noncommutative C*-algebras, With an appendix on Grothendieck's constants, J. Funct. Anal. 29 (1978), no. 3, 397-415.
    • (1978) J. Funct. Anal. , vol.29 , Issue.3 , pp. 397-415
    • Pisier, G.1
  • 117
    • 0001357908 scopus 로고
    • Probabilistic methods in the geometry of Banach spaces
    • Lecture Notes in Math., 1206 Springer, Berlin, 167-241
    • G. Pisier, Probabilistic methods in the geometry of Banach spaces, Probability and Analysis (Varenna, 1985), 167-241, Lecture Notes in Math., 1206, Springer, Berlin, 1986.
    • (1986) Probability and Analysis (Varenna, 1985)
    • Pisier, G.1
  • 118
    • 0001514006 scopus 로고
    • p1 and noncommutative generalizations
    • p1 and noncommutative generalizations, Math. Ann. 276 (1986), no. 1, 105-136.
    • (1986) Math. Ann. , vol.276 , Issue.1 , pp. 105-136
    • Pisier, G.1
  • 120
    • 84976111970 scopus 로고
    • The dual J* of the James space has cotype 2 and the Gordon-Lewis property
    • G. Pisier, The dual J* of the James space has cotype 2 and the Gordon-Lewis property, Math. Proc. Cambridge Philos. Soc. 103 (1988), 323-331.
    • (1988) Math. Proc. Cambridge Philos. Soc. , vol.103 , pp. 323-331
    • Pisier, G.1
  • 121
    • 0010963623 scopus 로고
    • Multipliers and lacunary sets in non-amenable groups
    • G. Pisier, Multipliers and lacunary sets in non-amenable groups, Amer. J. Math. 117 (1995), no. 2, 337-376.
    • (1995) Amer. J. Math. , vol.117 , Issue.2 , pp. 337-376
    • Pisier, G.1
  • 122
    • 0000136807 scopus 로고    scopus 로고
    • A simple proof of a theorem of Kirchberg and related results on C*-norms
    • G. Pisier, A simple proof of a theorem of Kirchberg and related results on C*-norms, J. Operator Theory 35 (1996), 317-335.
    • (1996) J. Operator Theory , vol.35 , pp. 317-335
    • Pisier, G.1
  • 123
    • 0030195280 scopus 로고    scopus 로고
    • The operator Hilbert space OH, complex interpolation and tensor norms
    • G. Pisier, The operator Hilbert space OH, complex interpolation and tensor norms, Mem. Amer. Math. Soc. 122 (1996), no. 585, viii+103 pp.
    • (1996) Mem. Amer. Math. Soc. , vol.122 , Issue.585 , pp. 8-103
    • Pisier, G.1
  • 124
    • 0037538981 scopus 로고    scopus 로고
    • p-spaces and completely p-summing maps
    • p-spaces and completely p-summing maps, Astérisque No. 247 (1998), vi+131 pp.
    • (1998) Astérisque , vol.247 , pp. 5-131
    • Pisier, G.1
  • 127
    • 13244291524 scopus 로고    scopus 로고
    • Completely bounded maps into certain Hilbertian operator spaces
    • G. Pisier, Completely bounded maps into certain Hilbertian operator spaces, Int. Math. Res. Not. (2004), no. 74, 3983-4018.
    • (2004) Int. Math. Res. , Issue.74 , pp. 3983-4018
    • Pisier, G.1
  • 128
    • 64549147848 scopus 로고    scopus 로고
    • Remarks on the non-commutative Khintchine inequalities for 0 < p < 2
    • G. Pisier, Remarks on the non-commutative Khintchine inequalities for 0 < p < 2, J. Funct. Anal. 256 (2009), no. 12, 4128-4161
    • (2009) J. Funct. Anal , vol.256 , Issue.12 , pp. 4128-4161
    • Pisier, G.1
  • 129
    • 0036026040 scopus 로고    scopus 로고
    • Grothendieck's theorem for operator spaces
    • G. Pisier and D. Shlyakhtenko, Grothendieck's theorem for operator spaces, Invent. Math. 150 (2002), no. 1, 185-217.
    • (2002) Invent. Math. , vol.150 , Issue.1 , pp. 185-217
    • Pisier, G.1    Shlyakhtenko, D.2
  • 132
    • 44949178833 scopus 로고    scopus 로고
    • Combinatorial aspects of Connes's embedding conjecture and asymptotic distribution of traces of products of unitaries
    • Theta Ser. Adv. Math. 6 Theta, Bucharest
    • F. Rǎadulescu, Combinatorial aspects of Connes's embedding conjecture and asymptotic distribution of traces of products of unitaries, Operator Theory 20, 197-205, Theta Ser. Adv. Math. 6, Theta, Bucharest, 2006.
    • (2006) Operator Theory , vol.20 , pp. 197-205
    • Rǎdulescu, F.1
  • 133
    • 51849168818 scopus 로고    scopus 로고
    • Optimal algorithms and inapproximability results for every CSP?
    • ACM, New York, 245-254
    • P. Raghavendra, Optimal algorithms and inapproximability results for every CSP?, in STOC'08, 245-254, ACM, New York, 2008.
    • (2008) STOC'08
    • Raghavendra, P.1
  • 134
    • 70349138408 scopus 로고    scopus 로고
    • Towards computing the Grothendieck constant
    • P. Raghavendra and D. Steurer, Towards computing the Grothendieck constant. Proceedings of SODA. 2009, 525-534.
    • (2009) Proceedings of SODA , pp. 525-534
    • Raghavendra, P.1    Steurer, D.2
  • 135
    • 58449121326 scopus 로고    scopus 로고
    • p-spaces into preduals of finite von Neumann algebras
    • p-spaces into preduals of finite von Neumann algebras, Israel J. Math. 163 (2008), 1-27.
    • (2008) Israel J. Math. , vol.163 , pp. 1-27
    • Randrianantoanina, N.1
  • 138
    • 78650966941 scopus 로고    scopus 로고
    • Simulating quantum correlations with finite communication
    • O. Regev and B. Toner, Simulating quantum correlations with finite communication, SIAM J. Comput. 39 (2009/10), 1562-1580.
    • (2009) SIAM J. Comput. , vol.39 , pp. 1562-1580
    • Regev, O.1    Toner, B.2
  • 139
    • 51249191529 scopus 로고
    • A proof of the Grothendieck inequality
    • R. Rietz, A proof of the Grothendieck inequality, Israel J. Math. 19 (1974), 271-276.
    • (1974) Israel J. Math. , vol.19 , pp. 271-276
    • Rietz, R.1
  • 141
    • 0001103699 scopus 로고
    • Subspaces of C*-algebras
    • Z.J. Ruan, Subspaces of C*-algebras, J. Funct. Anal. 76 (1988), 217-230.
    • (1988) J. Funct. Anal. , vol.76 , pp. 217-230
    • Ruan, Z.J.1
  • 142
    • 0001263955 scopus 로고
    • The best constant in the Khintchine inequality for complex Steinhaus variables the case p = 1
    • J. Sawa, The best constant in the Khintchine inequality for complex Steinhaus variables, the case p = 1, Studia Math. 81 (1985), 107-126.
    • (1985) Studia Math , vol.81 , pp. 107-126
    • Sawa, J.1
  • 144
    • 84966257802 scopus 로고
    • Zonoids whose polars are zonoids
    • R. Schneider, Zonoids whose polars are zonoids, Proc. Amer. Math. Soc. 50 (1975), 365-368.
    • (1975) Proc. Amer. Math. Soc. , vol.50 , pp. 365-368
    • Schneider, R.1
  • 147
    • 0000913075 scopus 로고
    • On the best constants in the Khinchine inequality
    • S.U. Szarek, On the best constants in the Khinchine inequality, Studia Math. 58 (1976), 197-208.
    • (1976) Studia Math , vol.58 , pp. 197-208
    • Szarek, S.U.1
  • 149
    • 0000186166 scopus 로고
    • On the Rademacher averages and the moduli of convexity and smoothness of the Schatten classes Sp
    • N. Tomczak-Jaegermann, On the Rademacher averages and the moduli of convexity and smoothness of the Schatten classes Sp, Studia Math. 50 (1974), 163-182.
    • (1974) Studia Math , vol.50 , pp. 163-182
    • Tomczak-Jaegermann, N.1
  • 151
    • 84860301266 scopus 로고
    • The complex Grothendieck inequality for 2 × 2 matrices
    • A. Tonge, The complex Grothendieck inequality for 2 × 2 matrices, Bull. Soc. Math. Grèce (N.S.) 27 (1986), 133-136.
    • (1986) Bull. Soc. Math. Grèce (N. S.) , vol.27 , pp. 133-136
    • Tonge, A.1
  • 153
    • 34250250611 scopus 로고
    • Quantum generalizations of Bell's inequality
    • B.S. Tsirelson, Quantum generalizations of Bell's inequality, Lett. Math. Phys. 4 (1980), no. 2, 93-100.
    • (1980) Lett. Math. Phys. , vol.4 , Issue.2 , pp. 93-100
    • Tsirelson, B.S.1
  • 155
    • 0242384600 scopus 로고
    • Some results and problems on quantum Bell-type inequalities
    • B.S. Tsirelson, Some results and problems on quantum Bell-type inequalities, Hadronic J. Suppl. 8 (1993), no. 4, 329-345.
    • (1993) Hadronic J. Suppl. , vol.8 , Issue.4 , pp. 329-345
    • Tsirelson, B.S.1
  • 156
    • 84863101324 scopus 로고    scopus 로고
    • Problem 33, 6 July Open Problems in Quantum Information Theory, Institut für Mathematische Physik, TU Braunschweig Germany
    • B.S. Tsirelson, Bell inequalities and operator algebras, Problem 33, 6 July 2006, Open Problems in Quantum Information Theory, Institut für Mathematische Physik, TU Braunschweig, Germany.
    • (2006) Bell inequalities and operator algebras
    • Tsirelson, B.S.1
  • 157
    • 84863103267 scopus 로고
    • Formulation of Bell type problems, and "noncommutative" convex geometry
    • Adv. Soviet Math. 9 Amer. Math. Soc., Providence, RI, 95-114
    • A.M. Vershik and B.S. Tsirelson, Formulation of Bell type problems, and "noncommutative" convex geometry, Representation Theory and Dynamical Systems, 95-114, Adv. Soviet Math. 9, Amer. Math. Soc., Providence, RI, 1992.
    • (1992) Representation Theory and Dynamical Systems
    • Vershik, A.M.1    Tsirelson, B.S.2
  • 159
    • 34948864613 scopus 로고
    • On tensor products of certain group C*-algebras
    • S. Wassermann, On tensor products of certain group C*-algebras, J. Funct. Anal. 23 (1976), 239-254.
    • (1976) J. Funct. Anal. , vol.23 , pp. 239-254
    • Wassermann, S.1
  • 160
    • 0008004485 scopus 로고
    • On generators for von Neumann algebras
    • W. Wogen, On generators for von Neumann algebras, Bull. Amer. Math. Soc. 75 (1969), 95-99.
    • (1969) Bull. Amer. Math. Soc. , vol.75 , pp. 95-99
    • Wogen, W.1
  • 161
    • 0013542507 scopus 로고
    • Applications du théorème de factorisation pour des fonctions à valeurs opérateurs
    • Q. Xu, Applications du théorème de factorisation pour des fonctions 'a valeurs opérateurs, Studia Math. 95 (1990), 273-292.
    • (1990) Studia Math , vol.95 , pp. 273-292
    • Xu, Q.1
  • 162
    • 33644815315 scopus 로고    scopus 로고
    • p-spaces
    • p-spaces, Duke Math. J. 131 (2006), 525-574.
    • (2006) Duke Math. J. , vol.131 , pp. 525-574
    • Xu, Q.1
  • 163
    • 33645563701 scopus 로고    scopus 로고
    • p-spaces 1 ≤ p ≤ q ≤ 2
    • p-spaces, 1 ≤ p ≤ q ≤ 2, Math. Ann. 335 (2006), 109-131. MR2217686 (2007m:46095)
    • (2006) Math. Ann , vol.335 , pp. 109-131
    • Xu, Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.