Pointwise uniformly rotund norms

Proceedings of the American Mathematical Society

Volumn 133, Issue 8, 2005, Pages 2259-2266

  Rychtář, Jan ^a,b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b UNIVERSITY OF NORTH CAROLINA AT GREENSBORO   (United States)

Author keywords

Descriptive compacts; Fragmentability; Pointwise uniformly rotund norm; Strictly positive measure; Uniform eberlein compacts

Indexed keywords

EID: 23744497739     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-05-07984-0     Document Type: Article

References (21)

1. S. Argyros, V. Farmaki: On the structure of weakly compact subsets of Hilbert spaces and application to the geometry of Banach spaces, Trans. Amer. Math. Soc. 289 (1985), 409-427. MR0779073 (86h:46023)
2. D. Amir and J. Lindenstrauss: The structure of weakly compact sets in Banach spaces, Ann. of Math. (2) 88 (1968), 35-46. MR0228983 (37:4562)
3. Y. Benyamini and T. Starbird: Embedding weakly compact sets into Hilbert space, Israel J. Math. 23 (1976), no. 2, 137-141. MR0397372 (53:1231)
4. W. W. Comfort and S. Negrepontis: Chain conditions in Topology, Cambridge Tracts in Mathematics 79, Cambridge University Press, 1982. MR0665100 (84k:04002)
5. R. Deville, G. Godefroy and V. Zizler: Smoothness and renormings in Banach spaces, Monographs and Surveys in Pure and Applied Mathematics 64, Pitman, 1993. MR1211634 (94d:46012)
6. S. J. Dilworth, D. Kutzarova and S. L. Troyanski: On some uniform geometric properties in function spaces, General topology in Banach spaces, 127-135, Nova Sci. Publ., Huntington, NY, 2001. MR1901540 (2003e:46035)
7. M. Fabian: Gâteaux differentiability of convex functions and topology. Weak Asplund spaces. Canadian Mathematical Society Series of Monographs and Advanced Texts. A Wiley-Interscience Publication. John Wiley and Sons, Inc., New York, 1997 MR1461271 (98h:46009)
8. M. Fabian, G. Godefroy and V. Zizler: The structure of uniformly Gâteaux smooth Banach spaces, Israel J. Math. 124 (2001), 243-252. MR1856517 (2002g:46015)
9. M. Fabian, P. Habala, P. Hájek, V. Montesinos, J. Pelant and V. Zizler: Functional analysis and infinite dimensional geometry, Canadian Math. Soc. Books (Springer-Verlag), 2001. MR1831176 (2002f:46001)
10. M. Fabian, V. Montesinos and V. Zizler: Biorthogonal systems in weakly Lindelöf spaces, submitted.
11. R. Haydon: Trees in renorming theory, Proc. London Math. Soc. (3) 78 (1999), 541-584. MR1674838 (2000d:46011)
12. K. John and V. Zizler: Smoothness and its equivalence in weakly compactly generated Banach spaces, J. Funct. Anal. 15 (1974), 161-166. MR0417759 (54:5807)
13. 1 which is uniformly convex in every direction, Constructive Theory of Functions, Sofia 84 (1984), 507-512.
14. D. N. Kutzarova and S. L. Troyanski: Reflexive Banach spaces without equivalent norms which are uniformly convex or uniformly differentiate in every direction, Studia Math. 72 (1982), no. 1, 91-95. MR0665893 (83k:46024)
15. H. E. Lacey: The isometric theory of classical Banach spaces, Die Grundlehren der mathematischen Wissenschaften, Band 208. Springer-Verlag, New York-Heidelberg, 1974. MR0493279 (58:12308)
16. I. Namioka: Pragmentability in Banach spaces. Interaction of topologies, Lecture Notes, Paseky School, Czech Republic (1999).
17. ∞(μ) for finite measures μ, Acta Math. 124 (1970), 205-248. MR0257721 (41:2370)
18. M. Raja: Weak* locally uniformly rotund norms and descriptive compact spaces, J. of Functional Analysis 197 (2003), 1-13. MR1957673 (2004a:46009)
19. J. Rychtář: Renorming of C(K) spaces, Proc. Amer. Math. Soc., 131 (2003), no. 7, 2063-2070 (electronic). MR1963751 (2004b:46018)
20. M. A. Smith: Banach spaces that are uniformly rotund in weakly compact sets of directions, Can. J. Math. 29, No. 5 (1977), 963-970. MR0450942 (56:9232)
21. S. Todorčević: Compact subsets of the first Baire class, J. Amer. Math. Soc. 12 (1999), no. 4, 1179-1212. MR1685782 (2000d:54028)