The structure of uniformly Gâteaux smooth Banach spaces

Israel Journal of Mathematics

Volumn 124, Issue , 2001, Pages 243-252

  Fabian, Marián ^a   Godefroy, Gilles ^b   Zizler, Václav ^a,c  

^a MATHEMATICAL INSTITUTE   (Czech Republic)

^b SORBONNE UNIVERSITÉ   (France)

^c UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035650052     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02772620     Document Type: Article

References (37)

1. D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Annals of Mathematics 88 (1968), 35-44.
2. S. Argyros and V. Farmaki, On the structure of weakly compact subsets of Hilbert, spaces and applications to the geometry of Banach spaces, Transactions of the American Mathematical Society 289 (1985), 409-427.
3. S. Argyros and S. Mercourakis, On weakly Lindelöf Banach spaces, Rocky Mountain Journal of Mathematics 23 (1993), 395-446.
4. Y. Benyamini, M. E. Rudin and M. Wage, Continuous images of weakly compact subsets of Banach spaces, Pacific Journal of Mathematics 70 (1977), 309-324.
5. Y. Benyamini and T. Starbird, Embedding weakly compact sets into Hilbert spaces, Israel Journal of Mathematics 23 (1976), 137-141.
6. W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński, Factoring weakly compact operators, Journal of Functional Analysis 17 (1974), 311-327.
7. R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs 64, Longman, London, 1993.
8. P. Enflo, Banach spaces which can be given an equivalent uniformly convex norm, Israel Journal of Mathematics 13 (1972), 281-288.
9. M. Fabian, Gâteaux Differentiability of Convex Functions and Topology. Weak Asplund Spaces, Wiley, New York, 1997.
10. M. Fabian, P. Hájek and V. Zizler, Uniform Eberlein compacta and uniformly Gâteaux smooth norms, Serdica Mathematical Journal 23 (1997), 351-362.
11. M. Fabian, V. Montesinos and V. Zizler, Pointwise semicontinuous smooth norms, to appear.
12. n)-smooth norms on separable Banach spaces, Czechoslovak Mathematical Journal 49 (1999), 657-672.
13. Γ), Fundament a Mathematicae 128 (1987), 15-28.
14. J. Frontisi, Representable Banach spaces and uniformly Gâteaux smooth norms, Serdica Mathematical Journal 22 (1996), 33-38.
15. G. Godefroy, Renormings of Banach spaces, in Handbook on Banach Spaces (W. B. Johnson and J. Lindenstrauss, eds.), Elsevier, Amsterdam, to appear.
16. P. Habala, P. Hájek and V. Zizler, Introduction to Banach Spaces I, II, Matfyzpress, Prague, 1996.
17. P. Hájek, Polynomials and injections of Banach spaces into superreflexive spaces, Archiv der Mathematik 63 (1994), 39-44.
18. P. Hájek, Dual renormings of Banach spaces, Commentationes Mathematicae Universitatis Carolinae 37 (1996), 241-253.
19. R. Haydon, Trees in renorming theory, Proceedings of the London Mathematical Society 78 (1999), 541-584.
20. W. B. Johnson and J. Lindenstrauss, Some remarks on weakly compactly generated Banach spaces, Israel Journal of Mathematics 17 (1974), 219-230 and 32 (1979), 382-383.
21. W. B. Johnson and J. Lindenstrauss, Some remarks on weakly compactly generated Banach spaces, Israel Journal of Mathematics 17 (1974), 219-230 and 32 (1979), 382-383.
22. D. Kutzarova and S. Troyanski, Reflexive Banach spaces without equivalent norms which are uniformly convex or uniformly different table in every direction, Studia Mathematica 72 (1982), 92-95.
23. J. Lindenstrauss, Weakly compact sets, their topological properties and the Banach spaces they generate, Annals of Mathematics Studies 69, Princeton University Press, 1972, pp. 235-276.
24. S. Mercourakis and S. Negrepontis, Banach spaces and Topology II, in Recent Progress in General Topology (M. Hušek and J. van Mill, eds.), Elsevier Science Publishers B.V., Amsterdam, 1992.
25. D. P. Milman, On some criteria for the regularity of spaces of type (B), Doklady Akademii Nauk SSSR 20 (1938), 243-246.
26. A. Moltó, V. Montesinos, J. Orihuela and S. Troyanski, Weakly uniformly rotund Banach spaces, Commentationes Mathematicae Universitatis Carolinae 39 (1998), 749-753.
27. A. Moltó and S. Troyanski, On uniformly Gâteaux differentiate norms in C(K), Mathematika 41 (1994), 233-238.
28. J. Orihuela, On weakly Lindelöf Banach spaces, in Progress in Functional Analysis (K. D. Bierstedt, J. Bonet, J. Horváth and M. Maestre, eds.), Elsevier Science Publishers, Amsterdam, 1992, pp. 279-291.
29. J. Orihuela and M. Valdivia, Projective generators and resolutions of identity in Banach spaces, Revista Matemática de la Universidad Complutense de Madrid 2, Suppl. Issue, 1990, pp. 179-199.
30. B. J. Pettis, A proof that every uniformly convex space is reflexive, Duke Mathematical Journal 5 (1939), 249-253.
31. H. P. Rosenthal, The heredity problem for weakly compactly generated Banach spaces, Compositio Mathematica 28 (1974), 83-111.
32. M. Talagrand, Espaces de Banach faiblement K-analytiques, Annals of Mathematics 110 (1979), 407-438.
33. W. K. Tang, Uniformly differentiate bump functions, Archiv der Mathematik 68 (1997), 55-59.
34. S. Troyanski, On uniform rotundity and smoothness in every direction in non-separable Banach spaces with unconditional basis, Comptes Rendus de l'Académie Bulgare des Sciences 30 (1977), 1243-1246.
35. J. Vanderwerff, J. H. M. Whitfield and V. Zizler, Markushevich bases and Corson compacta in duality, Canadian Journal of Mathematics 46 (1994), 200-211.
36. L. Vašák, On one generalization of weakly compactly generated Banach spaces, Studia Mathematica 70 (1981), 11-19.
37. V. Zizler, Nonseparable Banach spaces, in Handbook on Banach Spaces (W. B. Johnson and J. Lindenstrauss, eds.), Elsevier, Amsterdam, to appear.