메뉴 건너뛰기




Volumn 2, Issue , 2003, Pages 1201-1246

Chapter 28 Quotients of finite-dimensional banach spaces; random phenomena

Author keywords

[No Author keywords available]

Indexed keywords


EID: 67649516714     PISSN: 18745849     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-5849(03)80035-9     Document Type: Chapter
Times cited : (40)

References (60)
  • 1
    • 0003361152 scopus 로고
    • Normed Spaces with a Weak-Gordon-Lewis Property
    • Springer
    • Ball K. Normed Spaces with a Weak-Gordon-Lewis Property. Lecture Notes in Math. 1470 (1991), Springer
    • (1991) Lecture Notes in Math. 1470
    • Ball, K.1
  • 2
    • 84968466575 scopus 로고
    • Real isomorphic complex spaces need not to be complex isomorphic
    • Bourgain J. Real isomorphic complex spaces need not to be complex isomorphic. Proc. Amer. Math. Soc. 96 (1986) 221-226
    • (1986) Proc. Amer. Math. Soc. , vol.96 , pp. 221-226
    • Bourgain, J.1
  • 3
    • 67649466290 scopus 로고    scopus 로고
    • J. Bourgain, On finite-dimensional homogeneous Banach spaces, GAFA Israel Seminar 1986-87, Lecture Notes in Math. 1317, Springer, 232-239.
    • J. Bourgain, On finite-dimensional homogeneous Banach spaces, GAFA Israel Seminar 1986-87, Lecture Notes in Math. 1317, Springer, 232-239.
  • 4
    • 51249171950 scopus 로고
    • The Banach-Mazur distance to the cube and the Dvoretzky-Rogers factoriza-tion
    • Bourgain J., and Szarek S.J. The Banach-Mazur distance to the cube and the Dvoretzky-Rogers factoriza-tion. Israel J. Math. 62 (1988) 169-180
    • (1988) Israel J. Math. , vol.62 , pp. 169-180
    • Bourgain, J.1    Szarek, S.J.2
  • 6
    • 51249180463 scopus 로고
    • n and estimates of the Gordon-Lewis constant
    • n and estimates of the Gordon-Lewis constant. Israel J. Math. 37 (1980) 92-112
    • (1980) Israel J. Math. , vol.37 , pp. 92-112
    • Figiel, T.1    Johnson, W.B.2
  • 8
    • 0013205974 scopus 로고    scopus 로고
    • Euclidean structure infinite dimensional normed spaces
    • Johnson W.B., and Lindenstrauss J. (Eds), Elsevier, Amsterdam
    • Giannopoulos A.A., and Milman V.D. Euclidean structure infinite dimensional normed spaces. In: Johnson W.B., and Lindenstrauss J. (Eds). Handbook of the Geometry of Banach Spaces Vol. 1 (2001), Elsevier, Amsterdam 707-779
    • (2001) Handbook of the Geometry of Banach Spaces , vol.1 , pp. 707-779
    • Giannopoulos, A.A.1    Milman, V.D.2
  • 9
    • 0002582495 scopus 로고
    • The diameter of Minkowski compaction roughly equals to n
    • English translation
    • English translation. Gluskin E.D. The diameter of Minkowski compaction roughly equals to n. Functional Anal. Appl. 15 (1981) 57-58
    • (1981) Functional Anal. Appl. , vol.15 , pp. 57-58
    • Gluskin, E.D.1
  • 10
    • 0001396736 scopus 로고
    • Finite-dimensional analogues of spaces without basis
    • Gluskin E.D. Finite-dimensional analogues of spaces without basis. Dokl. Akad. Nauk SSSR 216 (1981) 1046-1050
    • (1981) Dokl. Akad. Nauk SSSR , vol.216 , pp. 1046-1050
    • Gluskin, E.D.1
  • 11
  • 12
    • 0002587601 scopus 로고
    • Absolutely summing operators and local unconditional structure
    • Gordon Y., and Lewis D.R. Absolutely summing operators and local unconditional structure. Acta Math. 133 (1974) 27-48
    • (1974) Acta Math. , vol.133 , pp. 27-48
    • Gordon, Y.1    Lewis, D.R.2
  • 14
    • 77956781055 scopus 로고    scopus 로고
    • Basic concepts in the geometry of Banach spaces
    • Johnson W.B., and Lindenstrauss J. (Eds), Elsevier, Amsterdam
    • Johnson W.B., and Lindenstrauss J. Basic concepts in the geometry of Banach spaces. In: Johnson W.B., and Lindenstrauss J. (Eds). Handbook of the Geometry of Banach Spaces Vol. 1 (2001), Elsevier, Amsterdam 1-84
    • (2001) Handbook of the Geometry of Banach Spaces , vol.1 , pp. 1-84
    • Johnson, W.B.1    Lindenstrauss, J.2
  • 16
    • 84935933925 scopus 로고
    • The proportional U.A.P. characterizes weak Hilbert spaces
    • Johnson W.B., and Pisier G. The proportional U.A.P. characterizes weak Hilbert spaces. J. London Math. Soc. 44 (1991) 525-536
    • (1991) J. London Math. Soc. , vol.44 , pp. 525-536
    • Johnson, W.B.1    Pisier, G.2
  • 17
    • 51249192500 scopus 로고
    • On bases finite-dimensional decompositions and weaker structures in Banach spaces
    • Johnson W.B., Rosenthal H.P., and Zippin M. On bases finite-dimensional decompositions and weaker structures in Banach spaces. Israel J. Math. 9 (1971) 488-506
    • (1971) Israel J. Math. , vol.9 , pp. 488-506
    • Johnson, W.B.1    Rosenthal, H.P.2    Zippin, M.3
  • 18
    • 0001387808 scopus 로고    scopus 로고
    • Sections of some finite-dimensional bodies and classes of smooth functions
    • Kashin B.S. Sections of some finite-dimensional bodies and classes of smooth functions. Izv. Akad. Nauk SSSR 41 (1997) 334-351
    • (1997) Izv. Akad. Nauk SSSR , vol.41 , pp. 334-351
    • Kashin, B.S.1
  • 19
    • 0033474309 scopus 로고    scopus 로고
    • Projection constants of symmetric spaces and variants of Khintchine's inequality
    • König H., Schütt C., and Tomczak-Jaegermann N. Projection constants of symmetric spaces and variants of Khintchine's inequality. J. Reine Angew. Math. 511 (1999) 1-42
    • (1999) J. Reine Angew. Math. , vol.511 , pp. 1-42
    • König, H.1    Schütt, C.2    Tomczak-Jaegermann, N.3
  • 22
    • 0037538383 scopus 로고
    • Finite-dimensional Banach spaces with symmetry constant of order √n
    • Mankiewicz P. Finite-dimensional Banach spaces with symmetry constant of order √n. Studia Math. 79 (1984) 193-200
    • (1984) Studia Math. , vol.79 , pp. 193-200
    • Mankiewicz, P.1
  • 23
    • 0010183801 scopus 로고
    • nwith applications to Gluskin spaces
    • nwith applications to Gluskin spaces. Studia Math. 88 (1988) 51-67
    • (1988) Studia Math. , vol.88 , pp. 51-67
    • Mankiewicz, P.1
  • 25
    • 51249176509 scopus 로고
    • A superreflexive Banach space X with L (X) admitting a homomorphism onto the Banach algebra C (β)
    • Mankiewicz P. A superreflexive Banach space X with L (X) admitting a homomorphism onto the Banach algebra C (β). Israel J. Math. 65 (1989) 1-16
    • (1989) Israel J. Math. , vol.65 , pp. 1-16
    • Mankiewicz, P.1
  • 28
    • 51249172400 scopus 로고
    • A superreflexive Banach space with a finite dimensional decomposition so that no large subspace has a basis
    • Mankiewicz P., and Nielsen N.J. A superreflexive Banach space with a finite dimensional decomposition so that no large subspace has a basis. Israel J. Math. 70 (1990) 188-204
    • (1990) Israel J. Math. , vol.70 , pp. 188-204
    • Mankiewicz, P.1    Nielsen, N.J.2
  • 30
    • 51249178417 scopus 로고
    • A solution of the finite-dimensional homogeneous Banach space problem
    • Mankiewicz P., and Tomczak-Jaegermann N. A solution of the finite-dimensional homogeneous Banach space problem. Israel J. Math. 75 (1991) 129-159
    • (1991) Israel J. Math. , vol.75 , pp. 129-159
    • Mankiewicz, P.1    Tomczak-Jaegermann, N.2
  • 33
    • 0030514775 scopus 로고    scopus 로고
    • Structural properties of weak cotype 2 spaces
    • Mankiewicz P., and Tomczak-Jaegermann N. Structural properties of weak cotype 2 spaces. Canad. J. Math. 48 (1996) 607-624
    • (1996) Canad. J. Math. , vol.48 , pp. 607-624
    • Mankiewicz, P.1    Tomczak-Jaegermann, N.2
  • 34
    • 0035561345 scopus 로고    scopus 로고
    • Families of random projections of symmetric convex bodies
    • Mankiewicz P., and Tomczak-Jaegermann N. Families of random projections of symmetric convex bodies. Geom. Funct. Anal. 11 (2001) 1282-1326
    • (2001) Geom. Funct. Anal. , vol.11 , pp. 1282-1326
    • Mankiewicz, P.1    Tomczak-Jaegermann, N.2
  • 35
    • 77957243206 scopus 로고    scopus 로고
    • Volumetric invariants and operators on random families of Banach spaces
    • to appear in
    • P. Mankiewicz and N. Tomczak-Jaegermann, Volumetric invariants and operators on random families of Banach spaces, to appear in Studia Math.
    • Studia Math
    • Mankiewicz, P.1    Tomczak-Jaegermann, N.2
  • 36
    • 0002090375 scopus 로고
    • Inégalité de Brunn-Minkowski inverse at applications à le théorie locale des espaces normés
    • Milman V.D. Inégalité de Brunn-Minkowski inverse at applications à le théorie locale des espaces normés. C.R. Acad. Sci. Paris Sér. I 302 (1986) 25-28
    • (1986) C.R. Acad. Sci. Paris Sér. I , vol.302 , pp. 25-28
    • Milman, V.D.1
  • 37
    • 14644439530 scopus 로고
    • The concentration phenomenon and linear structure of finite-dimensional normed spaces
    • Berkeley, CA, 1986, Amer. Math. Soc, Providence, RI
    • Milman V.D. The concentration phenomenon and linear structure of finite-dimensional normed spaces. Berkeley, CA, 1986. Proceedings of the International Congress of Mathematicians Vols. 1 (1987), Amer. Math. Soc, Providence, RI 961-975
    • (1987) Proceedings of the International Congress of Mathematicians , vol.1 , pp. 961-975
    • Milman, V.D.1
  • 38
    • 14644439530 scopus 로고
    • The concentration phenomenon and linear structure of finite-dimensional normed spaces
    • Berkeley, CA, 1986, Amer. Math. Soc, Providence, RI
    • Milman V.D. The concentration phenomenon and linear structure of finite-dimensional normed spaces. Berkeley, CA, 1986. Proceedings of the International Congress of Mathematicians Vols. 2 (1987), Amer. Math. Soc, Providence, RI 961-975
    • (1987) Proceedings of the International Congress of Mathematicians , vol.2 , pp. 961-975
    • Milman, V.D.1
  • 39
    • 51249170813 scopus 로고
    • Banach spaces with a weak cotype 2 property
    • Milman V.D., and Pisier G. Banach spaces with a weak cotype 2 property. Israel J. Math. 54 (1986) 139-158
    • (1986) Israel J. Math. , vol.54 , pp. 139-158
    • Milman, V.D.1    Pisier, G.2
  • 41
    • 38249026674 scopus 로고
    • Volume ratio and other s-numbers of operators related to local properties of Banach spaces
    • Pajor A., and Tomczak-Jaegermann N. Volume ratio and other s-numbers of operators related to local properties of Banach spaces. J. Func. Anal. 87 (1989) 273-293
    • (1989) J. Func. Anal. , vol.87 , pp. 273-293
    • Pajor, A.1    Tomczak-Jaegermann, N.2
  • 42
    • 67649481235 scopus 로고
    • Any separable Banach space with the bounded approximation property is a complemented subspace of a space with a basis
    • Pełczyński A. Any separable Banach space with the bounded approximation property is a complemented subspace of a space with a basis. Studia Math. 40 (1971) 133-139
    • (1971) Studia Math. , vol.40 , pp. 133-139
    • Pełczyński, A.1
  • 43
    • 0343924406 scopus 로고
    • Geometry of finite-dimensional Banach spaces and operator ideals
    • Lacey E. (Ed), Austin Univ. Press
    • Pełczyński A. Geometry of finite-dimensional Banach spaces and operator ideals. In: Lacey E. (Ed). Notes in Banach Spaces (1980), Austin Univ. Press 81-182
    • (1980) Notes in Banach Spaces , pp. 81-182
    • Pełczyński, A.1
  • 49
    • 0012913015 scopus 로고
    • The finite-dimensional basis problem with an appendix on nets of Grassman manifolds
    • Szarek S.J. The finite-dimensional basis problem with an appendix on nets of Grassman manifolds. Acta Math. 151 (1983) 153-179
    • (1983) Acta Math. , vol.151 , pp. 153-179
    • Szarek, S.J.1
  • 50
    • 0000602284 scopus 로고
    • On the existence and uniqueness of complex structure and spaces with "few" operators
    • Szarek S.J. On the existence and uniqueness of complex structure and spaces with "few" operators. Trans. Amer. Math. Soc. 293 (1986) 339-353
    • (1986) Trans. Amer. Math. Soc. , vol.293 , pp. 339-353
    • Szarek, S.J.1
  • 51
    • 84968467481 scopus 로고
    • A superreflexive space which does not admit complex structure
    • Szarek S.J. A superreflexive space which does not admit complex structure. Proc. Amer. Math. Soc. 97 (1986) 437-444
    • (1986) Proc. Amer. Math. Soc. , vol.97 , pp. 437-444
    • Szarek, S.J.1
  • 52
    • 0002786112 scopus 로고
    • A Banach space without a basis which has the bounded approximation property
    • Szarek S.J. A Banach space without a basis which has the bounded approximation property. Acta Math. 159 (1987) 81-98
    • (1987) Acta Math. , vol.159 , pp. 81-98
    • Szarek, S.J.1
  • 53
    • 0012962482 scopus 로고
    • n. and random matrices
    • n. and random matrices. Amer. J. Math. 112 (1990) 899-942
    • (1990) Amer. J. Math. , vol.112 , pp. 899-942
    • Szarek, S.J.1
  • 54
    • 0009400517 scopus 로고
    • Condition numbers of random matrices
    • Szarek S.J. Condition numbers of random matrices. J. Complexity 7 (1991) 131-149
    • (1991) J. Complexity , vol.7 , pp. 131-149
    • Szarek, S.J.1
  • 55
    • 67649466291 scopus 로고    scopus 로고
    • S.J. Szarek and M. Talagrand,0 An isomorphic version of the Sauer-Shelah lemma and the Banach-Mazur distance to the cube, GAFA Israel Seminar 1987-88, Lecture Notes in Math. 1376, Springer, 105-112
    • S.J. Szarek and M. Talagrand,0 An "isomorphic" version of the Sauer-Shelah lemma and the Banach-Mazur distance to the cube, GAFA Israel Seminar 1987-88, Lecture Notes in Math. 1376, Springer, 105-112
  • 56
    • 0001639987 scopus 로고
    • On nearly Euclidean decompositions of some classes of Banach spaces
    • Szarek S.J., and Tomczak-Jaegermann N. On nearly Euclidean decompositions of some classes of Banach spaces. Compositio Math. 40 (1980) 367-385
    • (1980) Compositio Math. , vol.40 , pp. 367-385
    • Szarek, S.J.1    Tomczak-Jaegermann, N.2
  • 57
    • 67649485827 scopus 로고    scopus 로고
    • Saturating constructions for normed spaces
    • in preparation
    • S.J. Szarek and N. Tomczak-Jaegermann, Saturating constructions for normed spaces, in preparation.
    • Szarek, S.J.1    Tomczak-Jaegermann, N.2
  • 58
    • 0003227837 scopus 로고
    • Banach-Mazur Distances and Finite Dimensional Operator Ideals
    • Longman, Harlow
    • Tomczak-Jaegermann N. Banach-Mazur Distances and Finite Dimensional Operator Ideals. Pitman Monographs (1989), Longman, Harlow
    • (1989) Pitman Monographs
    • Tomczak-Jaegermann, N.1
  • 59
    • 0000840166 scopus 로고
    • Characteristic vectors of bordered matrices with infinite dimensions
    • Wigner E. Characteristic vectors of bordered matrices with infinite dimensions. Ann. Math. 62 (1955) 548-564
    • (1955) Ann. Math. , vol.62 , pp. 548-564
    • Wigner, E.1
  • 60
    • 0001560594 scopus 로고
    • On the distribution of the roots of certain symmetric matrices
    • Wigner E. On the distribution of the roots of certain symmetric matrices. Ann. Math. 67 (1958) 325-327
    • (1958) Ann. Math. , vol.67 , pp. 325-327
    • Wigner, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.