Szlenk indices and uniform homeomorphisms

Transactions of the American Mathematical Society

Volumn 353, Issue 10, 2001, Pages 3895-3918

  Godefroy, G ^a   Kalton, N J ^b   Lancien, G ^c  

^a SORBONNE UNIVERSITÉ   (France)

^b UNIVERSITY OF MISSOURI   (United States)

^c UNIVERSITÉ DE FRANCHE COMTÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044531227     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-01-02825-2     Document Type: Article

References (28)

1. D. Alspach, The dual of the Bourgain-Delbaen space, Israel J. Math. 117 (2000) 239-259. MR 2001d:46022
2. D. Alspach, R. Judd and E. Odell, The Szlenk index and local li indices of a Danach space, to appear.
3. Y. Benyamini, The uniform classification of Banach spaces, Longhorn Notes, University of Texas Austin, 1984-5, pp. 15-38. MR 87a:46007
4. S.J. Dilworth, M. Girardi and D. Kutzarova, Banach spaces which admit a norm with the uniform Kadec-Klee property, Studia Math. 112 (1995) 267-277. MR 96a:46023
5. 0 and Lipschitz-homeomorphisms, Houston J. Math., to appear.
6. P. Enflo, Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math. 13 (1972) 281-288. MR 49:1073
7. 0(N) and Lipschitz isomorphisms, Geom. Funct. Anal. 10 (2000) 798-820. CMP 2001:03
8. G. Godefroy, N.J. Kalton and G. Lancien, L'espace de Banach c est déterminé par samétrique, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998) 817-822. MR 99h:46007
9. p, Israel J. Math. 87 (1994) 1-8. MR 95f:46028
10. R. Haydon, Subspaces of the Bourgain-Delbaen space, Studia Math. 139 (2000) 275-293. CMP 2000:13
11. S. Heinrich and P. Mankiewicz, Applications of ultrapowers to the uniform and Lipschitz classification of Banach spaces, Studia Math. 73 (1982) 225-251. MR 84h:46026
12. p, Compositio Mathematica, 34 (1977) 69-89. MR 56:12844
13. W.B. Johnson, J. Lindenstrauss, D. Preiss and G. Schcchtman, Almost Frechct differentiability of Lipschitz mappings between infinite dimensional Danach spaces, Preprint (2000).
14. W.B. Johnson, J. Lindenstrauss and G. Schechtman, Banach spaces determined by their uniform structure, Geom. Funct. Anal. 3 (1996) 430-470. MR 97b:4G016
15. p, Compositio Math. 28 (1974) 37-49. MR 50:5424
16. N.J. Kalton and M.M. Ostrovskii, Distances between Banach spaces, Forum Math. 11(1999), 17-48. MR 2000c:46024
17. N.J. Kalton and D. Werner, Property (M), M-ideals and almost isometric structure, J. Reine Angew. Math. 461 (1995) 137-178. MR 96m:46022
18. H. Knaust, E. Odell and T. Schlumprecht, On asymptotic structure, the Szlenk index and KK properties in Banach spaces, Positivity 3 (1999) 173-199. CMP 99:16
19. G. Landen, Théorie de l'indice et problèmes de renormage en géométrie des espaces de Banach, Thèse de doctorat de l'Université Paris VI, January 1992.
20. G. Lancien, On uniformly convex and uniformly Kadec-Klee renormings, Serdica Math. J. 21 (1995) 1-18. MR 96e:46009
21. G. Lancien, Réflexivité et normes duales possédant la propriété uniforme de Kadec-Klee, Publ. Math, de la Fac. des sciences de Besançon, Fasicule 14 (1993-94) 69-74.
22. 1(Γ), J. Functional Analysis 12 (1973) 177-187. MR 49:7731
23. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Vol. 1, Sequence spaces, SpringerVerlag, 1977. MR 58:17766
24. V. Milman, Geometric theory of Banach spaces. II. Geometry of the unit ball (Russian) Uspehi Mat. Nauk 26 (1971), 6 (162), 73-149. English translation: Russian Math. Surveys 26 (1971), 6, 79-163. MR 54:8240
25. 1, Israel J. Math. 20 (1975) 375-384. MR 51:13654
26. G. Pisier, Martingales with values in uniformly convex spaces, Israel J. Math. 20 (1975), 326-350. MR 52:14940
27. M. Ribe, Existence of separable uniformly homeomorphic non-isomorphic Banach spaces, Israel J. Math. 48 (1984), 139-147. MR 86e:46015
28. W. Szlenk, The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces, Studia Math. 30 (1968) 53-61. MR 37:3327