On the geometry of proportional quotients of l1m

Studia Mathematica

Volumn 155, Issue 1, 2003, Pages 51-66

  Mankiewicz, Piotr ^a   Szarek, Stanisław J ^b,c  

^a INSTITUTE OF MATHEMATICS   (Poland)

^b SORBONNE UNIVERSITÉ   (France)

^c CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038036656     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm155-1-4     Document Type: Article

References (23)

1. [B] K. Ball, Normed spaces with a weak-Gordon-Lewis property, in: Functional Analysis (Austin, TX, 1987/1989), Lecture Notes in Math. 1470, Springer, Berlin, 1991, 36-47.
2. [BKPS] P. Billard, S. Kwapień, A. Pełczyński and C. Samuel, Biorthogonal systems of random unconditional convergence in Banach spaces, in: Texas Functional Analysis Seminar 1985-1986 (Austin, TX, 1985-1986), Longhorn Notes, Univ. Texas, Austin, 1986, 13-35.
3. [Bo] J. Bourgain, On finite-dimensional homogeneous Banach spaces, in: GAFA Israel Seminar 1986-87, Lecture Notes in Math. 1317, Springer, 1988, 232-239.
4. [DS] K. R. Davidson and S. J. Szarek, Local operator theory, random matrices and Banach spaces, in: Handbook on the Geometry of Banach Spaces, Vol. 1, W. B. Johnson and J. Lindenstrauss (eds.), Elsevier, 2001, 317-366.
5. [FKP] T. Figiel, S. Kwapień and A. Pełczyński, Sharp estimates for the constants of local unconditional structure of Minkowski spaces, Bull. Acad. Polon. Sci. 25 (1977), 1221-1226.
6. [G] E. D. Gluskin, The diameter of Minkowski compactum is roughly equal to n, Funct. Anal. Appl. 15 (1981), no. 1, 57-58 (English transl.).
7. [K] B. S. Kashin, The widths of certain finite-dimensional sets and classes of smooth functions, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), 334-351 (in Russian).
8. [M1] P. Mankiewicz, Finite-dimensional Banach spaces with symmetry constant of order √n, Studia Math. 79 (1984), 193-200.
9. n, Israel J. Math. 109 (1999), 75-91.
10. [MT1] P. Mankiewicz and N. Tomczak-Jaegermann, A solution of the finite-dimensional homogeneous Banach space problem, Israel J. Math. 75 (1991), 129-159.
11. 2(X), Amer. J. Math. 116 (1994), 1341-1363.
12. [MT3] _, _, Quotients of finite-dimensional Banach spaces; random phenomena, in: Handbook on the Geometry of Banach Spaces, Vol. 2, W. B. Johnson and J. Lindenstrauss (eds.), Elsevier, to appear.
13. [MT4] _, _, Geometry of families of random projections of symmetric convex bodies, Geom. Funct. Anal. 11 (2001), 1282-1326.
14. [Mi1] V. D. Milman, A new proof of the theorem of A. Dvoretzky on sections of convex bodies, Funct. Anal. Appl. 5 (1971), no. 4, 28-37 (English transl.).
15. [Mi2] _, Randomness and pattern in convex geometric analysis, in: Proc. Internat. Congress Math., Vol. II (Berlin, 1998), Doc. Math. 1998, Extra Vol. II, 665-677.
16. [Mi2] _, Randomness and pattern in convex geometric analysis, in: Proc. Internat. Congress Math., Vol. II (Berlin, 1998), Doc. Math. 1998, Extra Vol. II, 665-677.
17. [MiS] V. D. Milman and G. Schechtman, Global versus local asymptotic theories of finite-dimensional normed spaces, Duke Math. J. 90 (1997), 73-93.
18. n, Bull. Acad. Polon. Sci. 26 (1978), 691-694.
19. [S2] _, The finite dimensional basis problem with an appendix on nets of Grassmann manifolds, Acta Math. 151 (1983), 153-179.
20. [S3] _, On the existence and uniqueness of complex structure and spaces with "few" operators, Trans. Amer. Math. Soc. 293 (1986), 339-353.
21. n, and random matrices, Amer. J. Math. 112 (1990), 899-942.
22. [S5] _, Condition numbers of random matrices, J. Complexity 7 (1991), 131-149.
23. [T] N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monogr. Surveys Pure Appl. Math. 38, Longman, Harlow, 1989.