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Volumn 2, Issue , 2006, Pages 1599-1621

Convexity, complexity, and high dimensions

Author keywords

Asymptotic geometric analysis; Complexity; Convex body; High dimension; Metric entropy

Indexed keywords

COMPLEXITY; CONVEX BODY; GEOMETRIC ANALYSIS; HIGH DIMENSIONS; METRIC ENTROPY;

EID: 84878084558     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper
Times cited : (20)

References (118)
  • 1
    • 4043147768 scopus 로고    scopus 로고
    • The Banach-Mazur compactum is an Aleksandrov compactification of a Q-manifold
    • Ageev, S. M., Bogatyǐ, S. A., Repovsh, D., The Banach-Mazur compactum is an Aleksandrov compactification of a Q-manifold. Mat. Zametki 76 (1) (2004), 3-10;
    • (2004) Mat. Zametki , vol.76 , Issue.1 , pp. 3-10
    • Ageev, S.M.1    Bogatyǐ, S.A.2    Repovsh, D.3
  • 2
    • 84878025543 scopus 로고    scopus 로고
    • English transl. Math. Notes 76 (1-2) (2004), 3-9.
    • (2004) Math. Notes , vol.76 , Issue.1-2 , pp. 3-9
  • 5
    • 33747188137 scopus 로고    scopus 로고
    • Approximating the cut-norm via Grothendieck's inequality
    • Alon, N., Naor, A., Approximating the Cut-Norm via Grothendieck's Inequality. SIAM J. Computing 35 (4) (2006), 787-803.
    • (2006) SIAM J. Computing , vol.35 , Issue.4 , pp. 787-803
    • Alon, N.1    Naor, A.2
  • 7
    • 35048868371 scopus 로고    scopus 로고
    • Small pseudo-random families of matrices: Derandomizing approximate quantum encryption
    • Lecture Notes in Comput. Sci. 3122, Springer-Verlag, Berlin
    • Ambainis, A., Smith, A., Small Pseudo-random Families of Matrices: Derandomizing Approximate Quantum Encryption. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques. Lecture Notes in Comput. Sci. 3122, Springer- Verlag, Berlin 2004, 249-260.
    • (2004) Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques , pp. 249-260
    • Ambainis, A.1    Smith, A.2
  • 8
    • 0442275925 scopus 로고    scopus 로고
    • Integral Kašin splittings
    • Anderson, G.W., Integral Kašin splittings. Israel J. Math. 138 (2003), 139-156.
    • (2003) Israel J. Math. , vol.138 , pp. 139-156
    • Anderson, G.W.1
  • 11
    • 33645900266 scopus 로고    scopus 로고
    • Logarithmic reduction of the level of randomness in some probabilistic constructions
    • Artstein-Avidan, S., Milman, V. D., Logarithmic reduction of the level of randomness in some probabilistic constructions. J. Funct. Anal. 235 (1) (2006), 297-329.
    • (2006) J. Funct. Anal. , vol.235 , Issue.1 , pp. 297-329
    • Artstein-Avidan, S.1    Milman, V.D.2
  • 12
    • 33745284883 scopus 로고
    • Comparison between plane symmetric convex bodies and parallelograms
    • Asplund, E., Comparison between plane symmetric convex bodies and parallelograms. Math. Scand. 8 (1960), 171-180.
    • (1960) Math. Scand. , vol.8 , pp. 171-180
    • Asplund, E.1
  • 13
    • 33144464230 scopus 로고    scopus 로고
    • Tensor products of convex sets and the volume of separable states on N qudits
    • Aubrun, G., Szarek, S. J., Tensor products of convex sets and the volume of separable states on N qudits. Phys. Rev. A. 73 (2006), 022109.
    • (2006) Phys. Rev. A. , vol.73 , pp. 022109
    • Aubrun, G.1    Szarek, S.J.2
  • 14
    • 0033358731 scopus 로고    scopus 로고
    • The flatness theorem for nonsymmetric convex bodies via the local theory of Banach spaces
    • Banaszczyk, W., Litvak, A. E., Pajor A., Szarek, S. J., The flatness theorem for nonsymmetric convex bodies via the local theory of Banach spaces. Math. Oper. Res. 24 (3) (1999), 728-750.
    • (1999) Math. Oper. Res. , vol.24 , Issue.3 , pp. 728-750
    • Banaszczyk, W.1    Litvak, A.E.2    Pajor, A.3    Szarek, S.J.4
  • 15
    • 54249110684 scopus 로고    scopus 로고
    • Random points, convex bodies, lattices
    • (Beijing, 2002), Higher Ed. Press, Beijing
    • Bárány, I., Random points, convex bodies, lattices. In Proceedings of the International Congress of Mathematicians (Beijing, 2002), Vol. III, Higher Ed. Press, Beijing 2002, 527-535.
    • (2002) Proceedings of the International Congress of Mathematicians , vol.3 , pp. 527-535
    • Bárány, I.1
  • 16
    • 0035351629 scopus 로고    scopus 로고
    • On polyhedral approximations of the second-order cone
    • Ben-Tal, A., Nemirovski, A., On polyhedral approximations of the second-order cone. Math. Oper. Res. 26 (2) (2001), 193-205.
    • (2001) Math. Oper. Res. , vol.26 , Issue.2 , pp. 193-205
    • Ben-Tal, A.1    Nemirovski, A.2
  • 18
    • 0000778931 scopus 로고
    • Bounded orthogonal systems and the (p)-set problem
    • Bourgain, J., Bounded orthogonal systems and the (p)-set problem. Acta Math. 162 (1989), 227-245.
    • (1989) Acta Math. , vol.162 , pp. 227-245
    • Bourgain, J.1
  • 21
    • 51249171950 scopus 로고
    • The Banach-Mazur distance to the cube and the Dvoretzky- Rogers factorization
    • Bourgain, J., Szarek, S.J., The Banach-Mazur distance to the cube and the Dvoretzky- Rogers factorization. Israel J. Math. 62 (2) (1988), 169-180.
    • (1988) Israel J. Math. , vol.62 , Issue.2 , pp. 169-180
    • Bourgain, J.1    Szarek, S.J.2
  • 25
    • 84878086016 scopus 로고    scopus 로고
    • [41], Addenda and corrigenda: Vol. 2, 1821
    • Diestel, J., Jarchow, H., Pietsch, A., Operator ideals. In [41], Vol. 1, 437-496; Addenda and corrigenda: Vol. 2, 1821.
    • Operator Ideals , vol.1 , pp. 437-496
    • Diestel, J.1    Jarchow, H.2    Pietsch, A.3
  • 26
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atomic decomposition
    • Donoho, D. L., Huo., X., Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory 47 (2001), 2845-2862.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 2845-2862
    • Donoho, D.L.1    Huo, X.2
  • 27
    • 0000660999 scopus 로고
    • The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
    • Dudley, R. M., The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1 (1967) 290-330.
    • (1967) J. Funct. Anal. , vol.1 , pp. 290-330
    • Dudley, R.M.1
  • 28
    • 0011183554 scopus 로고
    • Some results on convex bodies and Banach spaces
    • (Jerusalem, 1960), Jerusalem Academic Press, Jerusalem; Pergamon Press, Oxford
    • Dvoretzky, A., Some results on convex bodies and Banach spaces. In Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960), Jerusalem Academic Press, Jerusalem; Pergamon Press, Oxford, 1961, 123-160.
    • (1961) Proc. Internat. Sympos. Linear Spaces , pp. 123-160
    • Dvoretzky, A.1
  • 30
    • 0039397684 scopus 로고
    • A note on the Banach-Mazur distance to the cube
    • (Israel, 1992-1994), Oper. Theory Adv. Appl. 77, Birkhäuser, Basel
    • Giannopoulos, A. A., A note on the Banach-Mazur distance to the cube. In Geometric aspects of functional analysis (Israel, 1992-1994), Oper. Theory Adv. Appl. 77, Birkhäuser, Basel 1995, 67-73.
    • (1995) Geometric Aspects of Functional Analysis , pp. 67-73
    • Giannopoulos, A.A.1
  • 32
    • 0002582495 scopus 로고
    • The diameter of Minkowski compactum roughly equals to n
    • Gluskin, E. D., The diameter of Minkowski compactum roughly equals to n. Funct. Anal. Appl. 15 (1981), 57-58.
    • (1981) Funct. Anal. Appl. , vol.15 , pp. 57-58
    • Gluskin, E.D.1
  • 33
    • 0001396736 scopus 로고
    • Finite-dimensional analogues of spaces without a basis
    • Gluskin, E. D., Finite-dimensional analogues of spaces without a basis. Dokl. Akad. Nauk SSSR 261 (5) (1981), 1046-1050;
    • (1981) Dokl. Akad. Nauk SSSR , vol.261 , Issue.5 , pp. 1046-1050
    • Gluskin, E.D.1
  • 34
    • 0041084198 scopus 로고
    • English transl. Soviet Math. Dokl. 24 (3) (1981), 641-644.
    • (1981) Soviet Math. Dokl. , vol.24 , Issue.3 , pp. 641-644
  • 35
    • 38249037633 scopus 로고
    • Geometric and probabilistic estimates for entropy and approximation numbers of operators
    • Gordon, Y., König, H., Schütt, C., Geometric and probabilistic estimates for entropy and approximation numbers of operators. J. Approx. Theory 49 (3) (1987), 219-239.
    • (1987) J. Approx. Theory , vol.49 , Issue.3 , pp. 219-239
    • Gordon, Y.1    König, H.2    Schütt, C.3
  • 36
    • 27744584274 scopus 로고    scopus 로고
    • John's decomposition in the general case and applications
    • Gordon, Y., Litvak, A.E., Meyer, M., Pajor, A., John's Decomposition in the General Case and Applications. J. Differential Geom. 68 (1) (2004), 99-119.
    • (2004) J. Differential Geom. , vol.68 , Issue.1 , pp. 99-119
    • Gordon, Y.1    Litvak, A.E.2    Meyer, M.3    Pajor, A.4
  • 38
    • 5644232846 scopus 로고    scopus 로고
    • Randomizing quantum states: Constructions and applications
    • Hayden, P., Leung, D., Shor, P.W., Winter, A., Randomizing quantum states: Constructions and applications. Comm. Math. Phys. 250 (2) (2004), 371-391.
    • (2004) Comm. Math. Phys. , vol.250 , Issue.2 , pp. 371-391
    • Hayden, P.1    Leung, D.2    Shor, P.W.3    Winter, A.4
  • 39
    • 84972564751 scopus 로고
    • How well can an n .n matrix be approximated by reducible ones?
    • Herrero, D., Szarek, S. J., How well can an n .n matrix be approximated by reducible ones? Duke Math. J. 53 (1986), 233-248.
    • (1986) Duke Math. J. , vol.53 , pp. 233-248
    • Herrero, D.1    Szarek, S.J.2
  • 40
    • 0005141929 scopus 로고    scopus 로고
    • The semicircle law, free random variables and entropy
    • Amer. Math. Soc., Providence, RI
    • Hiai, F., Petz, D., The semicircle law, free random variables and entropy. Math. Surveys Monogr. 77, Amer. Math. Soc., Providence, RI, 2000.
    • (2000) Math. Surveys Monogr. , vol.77
    • Hiai, F.1    Petz, D.2
  • 41
    • 18444382009 scopus 로고    scopus 로고
    • The Knaster problem: More counterexamples
    • Hinrichs, A., Richter, C., The Knaster problem: more counterexamples. Israel J. Math. 145 (2005), 311-324.
    • (2005) Israel J. Math. , vol.145 , pp. 311-324
    • Hinrichs, A.1    Richter, C.2
  • 46
    • 0002282432 scopus 로고
    • Certain functionals on the Minkowski compactum
    • Kadets, M. ľ., Snobar, M. G., Certain functionals on the Minkowski compactum. Mat. Zametki 10 (1971), 453-457;
    • (1971) Mat. Zametki , vol.10 , pp. 453-457
    • Kadets, M.L.1    Snobar, M.G.2
  • 47
    • 34250470567 scopus 로고
    • English transl. Math. Notes 10 (1971), 694-696.
    • (1971) Math. Notes , vol.10 , pp. 694-696
  • 48
    • 0001387808 scopus 로고
    • The widths of certain finite-dimensional sets and classes of smooth functions
    • 478
    • Kashin, B. S., The widths of certain finite-dimensional sets and classes of smooth functions. Izv. Akad. Nauk SSSR (Ser.Mat.) 41 (2) (1977), 334-351, 478;
    • (1977) Izv. Akad. Nauk SSSR (Ser.Mat.) , vol.41 , Issue.2 , pp. 334-351
    • Kashin, B.S.1
  • 49
    • 84863331200 scopus 로고
    • English transl. Math. USSR-Izv. 11 (2) (1977), 317-333.
    • (1977) Math. USSR-Izv. , vol.11 , Issue.2 , pp. 317-333
  • 50
    • 18444395362 scopus 로고    scopus 로고
    • The Knaster problem and the geometry of high-dimensional cubes
    • Kashin, B.S., Szarek, S.J., The Knaster problem and the geometry of high-dimensional cubes. C. R. Math. Acad. Sci. Paris 336 (11) (2003), 931-936.
    • (2003) C. R. Math. Acad. Sci. Paris , vol.336 , Issue.11 , pp. 931-936
    • Kashin, B.S.1    Szarek, S.J.2
  • 51
    • 30744434916 scopus 로고    scopus 로고
    • On the gram matrices of systems of uniformly bounded functions
    • Kashin, B.S., Szarek, S.J., On the Gram Matrices of Systems of Uniformly Bounded Functions. Proc. Steklov Inst. Math. 243 (2003), 227-233
    • (2003) Proc. Steklov Inst. Math. , vol.243 , pp. 227-233
    • Kashin, B.S.1    Szarek, S.J.2
  • 52
    • 84878094944 scopus 로고    scopus 로고
    • Isomorphic and almost-isometric problems in high dimensional convex geometry
    • (Madrid, 2006), EMS Publishing House, Zürich
    • Klartag, B., Isomorphic and almost-isometric problems in high dimensional convex geometry. In Proceedings of the International Congress of Mathematicians (Madrid, 2006), Volume II, EMS Publishing House, Zürich 2006, 1547-1562.
    • (2006) Proceedings of the International Congress of Mathematicians , vol.2 , pp. 1547-1562
    • Klartag, B.1
  • 53
    • 0039365150 scopus 로고
    • Problem 4
    • Knaster, B., Problem 4. Colloq. Math. 30 (1947), 30-31.
    • (1947) Colloq. Math. , vol.30 , pp. 30-31
    • Knaster, B.1
  • 55
    • 0002729579 scopus 로고
    • On the covering numbers of convex bodies
    • Geometric aspects of functional analysis (1985-86), Springer-Verlag, Berlin, New York
    • König, H., Milman, V. D., On the covering numbers of convex bodies. In Geometric aspects of functional analysis (1985-86), Lecture Notes in Math. 1267, Springer-Verlag, Berlin, New York 1987, 82-95.
    • (1987) Lecture Notes in Math. , vol.1267 , pp. 82-95
    • König, H.1    Milman, V.D.2
  • 56
    • 0009148389 scopus 로고
    • Bounds for projection constants and 1-summing norms
    • König, H., Tomczak-Jaegermann, N., Bounds for projection constants and 1-summing norms. Trans. Amer. Math. Soc. 320 (2) (1990), 799-823.
    • (1990) Trans. Amer. Math. Soc. , vol.320 , Issue.2 , pp. 799-823
    • König, H.1    Tomczak-Jaegermann, N.2
  • 57
    • 0001461506 scopus 로고
    • Metric entropy and the small ball problem for Gaussian measures
    • Kuelbs, J., W.V. Li, Metric entropy and the small ball problem for Gaussian measures. J. Funct. Anal. 116 (1) (1993), 133-157.
    • (1993) J. Funct. Anal. , vol.116 , Issue.1 , pp. 133-157
    • Kuelbs, J.1    Li, W.V.2
  • 58
    • 0040775278 scopus 로고    scopus 로고
    • Approximation of convex bodies by centrally symmetric bodies
    • Lassak, M., Approximation of convex bodies by centrally symmetric bodies. Geom. Dedicata 72 (1) (1998), 63-68.
    • (1998) Geom. Dedicata , vol.72 , Issue.1 , pp. 63-68
    • Lassak, M.1
  • 61
    • 0003421887 scopus 로고
    • Discrete groups, expanding graphs and invariant measures. with an appendix by Jonathan D. Rogawski
    • Birkhäuser Verlag, Basel
    • Lubotzky, A. Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D. Rogawski. Progr. Math. 125, Birkhäuser Verlag, Basel 1994.
    • (1994) Progr. Math. , vol.125
    • Lubotzky, A.1
  • 64
    • 84973994559 scopus 로고
    • Random banach spaces. The limitations of the method
    • Corrigenda: Mathematica 42 (1995), 220-221
    • Mankiewicz, P., Szarek, S. J., Random Banach Spaces. The limitations of the method. Mathematica 41 (1994), 239-250; Corrigenda: Mathematica 42 (1995), 220-221.
    • (1994) Mathematica , vol.41 , pp. 239-250
    • Mankiewicz, P.1    Szarek, S.J.2
  • 65
    • 0000735690 scopus 로고
    • Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes
    • Marcus, M. B., Pisier, G., Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes. Acta Math. 152 (3-4) (1984), 245-301.
    • (1984) Acta Math. , vol.152 , Issue.3-4 , pp. 245-301
    • Marcus, M.B.1    Pisier, G.2
  • 66
  • 70
    • 0001921812 scopus 로고
    • Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
    • Maurey, B., Pisier, G., Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach. Studia Math. 58 (1) (1976), 45-90.
    • (1976) Studia Math. , vol.58 , Issue.1 , pp. 45-90
    • Maurey, B.1    Pisier, G.2
  • 72
    • 17744381831 scopus 로고    scopus 로고
    • Relaxation of quadratic programs in operator theory and system analysis
    • (Bordeaux, 2000), Oper. Theory Adv. Appl. 129, Birkhäuser, Basel
    • Megretski, A., Relaxation of Quadratic Programs in Operator Theory and System Analysis. In Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), Oper. Theory Adv. Appl. 129, Birkhäuser, Basel 2001, 365-392.
    • (2001) Systems, Approximation, Singular Integral Operators, and Related Topics , pp. 365-392
    • Megretski, A.1
  • 73
    • 0002417176 scopus 로고
    • A new proof of the theorem of A. Dvoretzky on sections of convex bodies
    • Milman, V. D., A new proof of the theorem of A. Dvoretzky on sections of convex bodies. Funct. Anal. Appl. 5 (1971), 28-37.
    • (1971) Funct. Anal. Appl. , vol.5 , pp. 28-37
    • Milman, V.D.1
  • 74
    • 84968520245 scopus 로고
    • Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space
    • Milman, V. D., Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space. Proc. Amer. Math. Soc. 94 (3) (1985), 445-449.
    • (1985) Proc. Amer. Math. Soc. , vol.94 , Issue.3 , pp. 445-449
    • Milman, V.D.1
  • 75
    • 14644439530 scopus 로고
    • The concentration phenomenon and linear structure of finite-dimensional normed spaces
    • (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, R.I.
    • Milman, V. D., The concentration phenomenon and linear structure of finite-dimensional normed spaces. In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), Vol. 2, Amer. Math. Soc., Providence, R.I., 1987, 961-975.
    • (1987) Proceedings of the International Congress of Mathematicians , vol.2 , pp. 961-975
    • Milman, V.D.1
  • 76
    • 0042244854 scopus 로고
    • A few observations on the connections between local theory and some other fields
    • Geometric aspects of functional analysis (1986/87), Springer-Verlag, Berlin
    • Milman, V. D., A few observations on the connections between local theory and some other fields. In Geometric aspects of functional analysis (1986/87), Lecture Notes in Math. 1317, Springer-Verlag, Berlin 1988, 283-289.
    • (1987) Lecture Notes in Math. , vol.1317 , pp. 283-289
    • Milman, V.D.1
  • 77
    • 0347386259 scopus 로고    scopus 로고
    • Surprising geometric phenomena in high-dimensional convexity theory
    • (Budapest, 1996). Progr. Math. 169, Birkhäuser, Basel
    • Milman, V. D., Surprising geometric phenomena in high-dimensional convexity theory. In European Congress of Mathematics (Budapest, 1996), Vol. II. Progr. Math. 169, Birkhäuser, Basel 1998, 73-91.
    • (1998) European Congress of Mathematics , vol.2 , pp. 73-91
    • Milman, V.D.1
  • 78
    • 0038552631 scopus 로고    scopus 로고
    • Randomness and pattern in convex geometric analysis
    • (Berlin, 1998), Doc. Math., J. DMV, Extra Vol. ICM Berlin
    • Milman, V. D., Randomness and pattern in convex geometric analysis. In Proceedings of the International Congress of Mathematicians (Berlin, 1998), Vol. II, Doc. Math., J. DMV, Extra Vol. ICM Berlin, 1998, 665-677.
    • (1998) Proceedings of the International Congress of Mathematicians , vol.2 , pp. 665-677
    • Milman, V.D.1
  • 79
    • 0034713470 scopus 로고    scopus 로고
    • Entropy and asymptotic geometry of non-symmetric convex bodies
    • Milman, V. D., Pajor, A., Entropy and asymptotic geometry of non-symmetric convex bodies. Adv. Math. 152 (2) (2000), 314-335.
    • (2000) Adv. Math. , vol.152 , Issue.2 , pp. 314-335
    • Milman, V.D.1    Pajor, A.2
  • 80
    • 0003656879 scopus 로고
    • Asymptotic theory of finite-dimensional normed spaces. with an appendix by M. Gromov
    • Springer-Verlag, Berlin
    • Milman, V. D., Schechtman, G. Asymptotic theory of finite-dimensional normed spaces. With an appendix by M. Gromov. Lecture Notes in Math. 1200, Springer-Verlag, Berlin 1986.
    • (1986) Lecture Notes in Math. , vol.1200
    • Milman, V.D.1    Schechtman, G.2
  • 81
    • 18044392721 scopus 로고    scopus 로고
    • A geometric approach to duality of metric entropy
    • Milman, V. D., Szarek, S. J., A geometric approach to duality of metric entropy. C. R. Acad. Sci. Paris Sér. I Math. 332 (2) (2001), 157-162.
    • (2001) C. R. Acad. Sci. Paris Sér. i Math. , vol.332 , Issue.2 , pp. 157-162
    • Milman, V.D.1    Szarek, S.J.2
  • 82
    • 70450155236 scopus 로고    scopus 로고
    • Advances in convex optimization: Conic programming
    • Madrid, EMSPublishing House, Zürich 2006/2007
    • Nemirovski, A., Advances in convex optimization: conic programming. In Proceedings of the International Congress of Mathematicians (Madrid, 2006), Volume I, EMSPublishing House, Zürich 2006/2007.
    • (2006) Proceedings of the International Congress of Mathematicians , vol.1
    • Nemirovski, A.1
  • 83
    • 38249026674 scopus 로고
    • Volume ratio and other s-numbers of operators related to local properties of Banach spaces
    • Pajor, A., Tomczak-Jaegermann, N., Volume ratio and other s-numbers of operators related to local properties of Banach spaces. J. Func. Anal. 87 (2) (1989), 273-293.
    • (1989) J. Func. Anal. , vol.87 , Issue.2 , pp. 273-293
    • Pajor, A.1    Tomczak-Jaegermann, N.2
  • 84
    • 0037874971 scopus 로고
    • Wissenschaftliche Beiträge der Friedrich-Schiller-Universität Jena, Friedrich-Schiller-Universität, Jena
    • Pietsch, A., Theorie der Operatorenideale (Zusammenfassung). Wissenschaftliche Beiträge der Friedrich-Schiller-Universität Jena, Friedrich-Schiller-Universität, Jena, 1972.
    • (1972) Theorie der Operatorenideale (Zusammenfassung)
    • Pietsch, A.1
  • 85
    • 0002054972 scopus 로고
    • Un théorème sur les opérateurs linéaires entre espaces de Banach qui se factorisent par un espace de Hilbert
    • Pisier, G., Un théorème sur les opérateurs linéaires entre espaces de Banach qui se factorisent par un espace de Hilbert. Ann. Sci. Ecole Norm. Sup. (4) 13 (1) (1980), 23-43
    • (1980) Ann. Sci. Ecole Norm. Sup. (4) , vol.13 , Issue.1 , pp. 23-43
    • Pisier, G.1
  • 86
    • 0003345901 scopus 로고
    • Remarques sur un résultat non publié de B. Maurey
    • Exp. No. V, École Polytechnique, Palaiseau
    • Pisier, G., Remarques sur un résultat non publié de B. Maurey. Séminaire d'Analyse Fonctionnelle, 1980-1981, Exp. No. V, École Polytechnique, Palaiseau 1981, 13 pp.
    • (1981) Séminaire D'Analyse Fonctionnelle, 1980-1981
    • Pisier, G.1
  • 87
    • 0001266043 scopus 로고
    • Holomorphic semigroups and the geometry of Banach spaces
    • Pisier, G., Holomorphic semigroups and the geometry of Banach spaces. Ann. of Math. (2) 115 (2) (1982), 375-392.
    • (1982) Ann. of Math. (2) , vol.115 , Issue.2 , pp. 375-392
    • Pisier, G.1
  • 88
    • 63049090829 scopus 로고
    • Finite rank projections on Banach spaces and a conjecture of Grothendieck
    • (Warszawa, 1983), PWN, Warsaw
    • Pisier, G., Finite rank projections on Banach spaces and a conjecture of Grothendieck. In Proceedings of the International Congress of Mathematicians (Warszawa, 1983), Vol. 2, PWN, Warsaw 1984, 1027-1039.
    • (1984) Proceedings of the International Congress of Mathematicians , vol.2 , pp. 1027-1039
    • Pisier, G.1
  • 89
    • 0003254209 scopus 로고
    • The volume of convex bodies and banach space geometry
    • Cambridge University Press, Cambridge
    • Pisier, G., The Volume of Convex Bodies and Banach Space Geometry. Cambridge Tracts in Math, 94, Cambridge University Press, Cambridge 1989.
    • (1989) Cambridge Tracts in Math , vol.94
    • Pisier, G.1
  • 90
    • 0001703669 scopus 로고
    • A new approach to several results of V. Milman
    • Pisier, G., A new approach to several results of V. Milman. J. Reine Angew. Math. 393 (1989), 115-131.
    • (1989) J. Reine Angew. Math. , vol.393 , pp. 115-131
    • Pisier, G.1
  • 91
    • 0040807711 scopus 로고    scopus 로고
    • Distances between non-symmetric convex bodies and the MM-estimate
    • Rudelson, M., Distances between non-symmetric convex bodies and the MM-estimate. Positivity 4 (2) (2000), 161-178.
    • (2000) Positivity , vol.4 , Issue.2 , pp. 161-178
    • Rudelson, M.1
  • 92
    • 33746801607 scopus 로고    scopus 로고
    • Geometric approach to error correcting codes and reconstruction of signals
    • Rudelson, M., Vershynin, R., Geometric approach to error correcting codes and reconstruction of signals. Internat. Math. Res. Notices 2005 (64) (2005), 4019-4041.
    • (2005) Internat. Math. Res. Notices , vol.2005 , Issue.64 , pp. 4019-4041
    • Rudelson, M.1    Vershynin, R.2
  • 93
    • 0001430981 scopus 로고
    • Trigonometric series with gaps
    • Rudin, W., Trigonometric series with gaps. J. Math. Mech. 9 (1960), 203-227.
    • (1960) J. Math. Mech. , vol.9 , pp. 203-227
    • Rudin, W.1
  • 94
    • 0003288907 scopus 로고
    • Some applications of modular forms
    • Cambridge University Press, Cambridge
    • Sarnak, P., Some applications of modular forms. Cambridge Tracts in Math. 99, Cambridge University Press, Cambridge 1990.
    • (1990) Cambridge Tracts in Math. , vol.99
    • Sarnak, P.1
  • 96
    • 0000581036 scopus 로고
    • Entropy numbers of diagonal operators between symmetric Banach spaces
    • Schütt, C., Entropy numbers of diagonal operators between symmetric Banach spaces. J. Approx. Theory 40 (2) (1984), 121-128.
    • (1984) J. Approx. Theory , vol.40 , Issue.2 , pp. 121-128
    • Schütt, C.1
  • 97
    • 3242887462 scopus 로고    scopus 로고
    • Polytopes with vertices chosen randomly from the boundary of a convex body
    • Lecture Notes in Math. 1807, Springer-Verlag, Berlin
    • Schütt, C., Werner, E., Polytopes with vertices chosen randomly from the boundary of a convex body. In Geometric aspects of functional analysis, Lecture Notes in Math. 1807, Springer-Verlag, Berlin 2003, 241-422.
    • (2003) Geometric Aspects of Functional Analysis , pp. 241-422
    • Schütt, C.1    Werner, E.2
  • 99
    • 0013120966 scopus 로고    scopus 로고
    • Limit distributions of matrices with bosonic and fermionic entries
    • (Waterloo, ON, 1995), Fields Inst. Commun. 12, Amer. Math. v Soc., Providence, RI
    • Shlyakhtenko, D., Limit distributions of matrices with bosonic and fermionic entries. In Free probability theory (Waterloo, ON, 1995), Fields Inst. Commun. 12, Amer. Math. v Soc., Providence, RI, 1997, 241-252.
    • (1997) Free Probability Theory , pp. 241-252
    • Shlyakhtenko, D.1
  • 100
    • 0002329959 scopus 로고
    • Gaussian random processes, and measures of solid angles in Hilbert space
    • Sudakov, V.N., Gaussian random processes, and measures of solid angles in Hilbert space. Dokl. Akad. Nauk SSSR 197 (1971), 43-45;
    • (1971) Dokl. Akad. Nauk SSSR , vol.197 , pp. 43-45
    • Sudakov, V.N.1
  • 101
    • 0000820132 scopus 로고
    • English transl. Soviet Math. Dokl. 12 (1971), 412-415.
    • (1971) Soviet Math. Dokl. , vol.12 , pp. 412-415
  • 103
    • 0012913015 scopus 로고
    • The finite-dimensional basis problem with an appendix on nets of Grassmann manifolds
    • Szarek, S. J., The finite-dimensional basis problem with an appendix on nets of Grassmann manifolds. Acta Math. 151 (3-4) (1983), 153-179.
    • (1983) Acta Math. , vol.151 , Issue.3-4 , pp. 153-179
    • Szarek, S.J.1
  • 104
    • 0012962482 scopus 로고
    • n and random matrices
    • n and random matrices. Amer. J. Math. 112 (6) (1990), 899-942.
    • (1990) Amer. J. Math. , vol.112 , Issue.6 , pp. 899-942
    • Szarek, S.J.1
  • 105
    • 38249018829 scopus 로고
    • An exotic quasidiagonal operator
    • Szarek, S. J., An exotic quasidiagonal operator. J. Funct. Anal. 89 (1990), 274-290.
    • (1990) J. Funct. Anal. , vol.89 , pp. 274-290
    • Szarek, S.J.1
  • 106
    • 28844465382 scopus 로고    scopus 로고
    • The volume of separable states is super-doubly-exponentially small in the number of qubits
    • Szarek, S. J., The volume of separable states is super-doubly- exponentially small in the number of qubits. Phys. Rev. A 72 (2005), 032304.
    • (2005) Phys. Rev. A , vol.72 , pp. 032304
    • Szarek, S.J.1
  • 107
    • 0000887263 scopus 로고
    • An "isomorphic" version of the Sauer-Shelah lemma and the Banach-Mazur distance to the cube
    • Lecture Notes in Math. 1376, Springer-Verlag, Berlin
    • Szarek, S. J., Talagrand, M., An "isomorphic" version of the Sauer-Shelah lemma and the Banach-Mazur distance to the cube. In Geometric aspects of functional analysis (1987- 88), Lecture Notes in Math. 1376, Springer-Verlag, Berlin 1989, 105-112.
    • (1989) Geometric Aspects of Functional Analysis (1987-88) , pp. 105-112
    • Szarek, S.J.1    Talagrand, M.2
  • 108
    • 0001639987 scopus 로고
    • On nearly Euclidean decomposition for some classes of Banach spaces
    • Szarek, S. J., Tomczak-Jaegermann, N., On nearly Euclidean decomposition for some classes of Banach spaces. Compositio Math. 40 (3) (1980), 367-385.
    • (1980) Compositio Math. , vol.40 , Issue.3 , pp. 367-385
    • Szarek, S.J.1    Tomczak-Jaegermann, N.2
  • 109
    • 14644414499 scopus 로고    scopus 로고
    • Saturating constructions for normed spaces
    • Szarek, S. J., Tomczak-Jaegermann, N., Saturating constructions for normed spaces. Geom. Funct. Anal. 14 (6) (2004), 1352-1375.
    • (2004) Geom. Funct. Anal. , vol.14 , Issue.6 , pp. 1352-1375
    • Szarek, S.J.1    Tomczak-Jaegermann, N.2
  • 110
    • 14644427208 scopus 로고    scopus 로고
    • Saturating constructions for normed spaces II
    • Szarek, S. J., Tomczak-Jaegermann, N., Saturating constructions for normed spaces II. J. Funct. Anal. 221 (2) (2005), 407-438.
    • (2005) J. Funct. Anal. , vol.221 , Issue.2 , pp. 407-438
    • Szarek, S.J.1    Tomczak-Jaegermann, N.2
  • 112
    • 0008293253 scopus 로고
    • Sections of smooth convex bodies via majorizing measures
    • Talagrand, M., Sections of smooth convex bodies via majorizing measures. Acta Math. 175 (1995), 273-300.
    • (1995) Acta Math. , vol.175 , pp. 273-300
    • Talagrand, M.1
  • 113
    • 0001499209 scopus 로고
    • Dualité des nombres d'entropie pour des opérateurs à valeurs dans un espace de Hilbert. (French)
    • Tomczak-Jaegermann, N., Dualité des nombres d'entropie pour des opérateurs à valeurs dans un espace de Hilbert. (French) C. R. Acad. Sci. Paris Sér. I Math. 305 (7) (1987), 299-301.
    • (1987) C. R. Acad. Sci. Paris Sér. i Math. , vol.305 , Issue.7 , pp. 299-301
    • Tomczak-Jaegermann, N.1
  • 114
    • 0003227837 scopus 로고
    • Banach-Mazur distances and finite-dimensional operator ideals
    • Longman, Harlow; Wiley, New York
    • Tomczak-Jaegermann, N., Banach-Mazur distances and finite-dimensional operator ideals. Pitman Monogr. Surveys Pure Appl. Math. 38, Longman, Harlow;Wiley, New York 1989.
    • (1989) Pitman Monogr. Surveys Pure Appl. Math. , vol.38
    • Tomczak-Jaegermann, N.1
  • 115
    • 0001885497 scopus 로고
    • Property T and approximations of operators
    • Voiculescu, D., Property T and approximations of operators. Bull. London Math. Soc. 22 (1990), 25-30.
    • (1990) Bull. London Math. Soc. , vol.22 , pp. 25-30
    • Voiculescu, D.1
  • 116
    • 0000215544 scopus 로고
    • Limit laws for random matrices and free products
    • Voiculescu, D., Limit laws for random matrices and free products. Invent. Math. 104 (1991), 201-220.
    • (1991) Invent. Math. , vol.104 , pp. 201-220
    • Voiculescu, D.1
  • 117
    • 0003385937 scopus 로고
    • Free probability theory: Random matrices and von Neumann algebras
    • (Zürich), Birkhäuser, Basel
    • Voiculescu, D., Free probability theory: random matrices and von Neumann algebras. In Proceedings of the International Congress of Mathematicians (Zürich, 1994), Vol. 1, Birkhäuser, Basel 1995, 227-241.
    • (1994) Proceedings of the International Congress of Mathematicians , vol.1 , pp. 227-241
    • Voiculescu, D.1
  • 118
    • 0003341428 scopus 로고
    • Free random variables. A non commutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups
    • Amer. Math. Soc., Providence, RI
    • Voiculescu, D., Dykema, K., Nica, A., Free random variables. A non commutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. CRM Monogr. Ser. 1, Amer. Math. Soc., Providence, RI, 1992.
    • (1992) CRM Monogr. Ser. , vol.1
    • Voiculescu, D.1    Dykema, K.2    Nica, A.3


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