Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Renorming of $C(K)$ spaces

Author: Jan Rychtár
Journal: Proc. Amer. Math. Soc. 131 (2003), 2063-2070
MSC (2000): Primary 46B03, 46E10
Published electronically: February 5, 2003
MathSciNet review: 1963751
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If $K$ is a scattered Eberlein compact space, then $C(K)^{*}$ admits an equivalent dual norm that is uniformly rotund in every direction. The same is shown for the dual to the Johnson-Lindenstrauss space $\text{JL}_{2}$.

References [Enhancements On Off] (What's this?)

  • [1] K. Alster, Some remarks on Eberlein compacts, Fundamenta Mathematicae 104 (1979), 43-46. MR 80k:54035
  • [2] S. Argyros and V. Farmaki, On the structure of weakly compact subsets of Hilbert spaces and applications to the geometry of Banach spaces, Trans. Amer. Math. Soc. 289 (1985), 409-427. MR 86h:46023
  • [3] Y. Benyamini, M. E. Rudin and M. Wage, Continuous images of weakly compact subsets of Banach spaces, Pacific J. Math. 70 (1977), 309-324. MR 58:30065
  • [4] J.M.F Castillo and M. González, Three space problems in Banach space theory, Lecture Notes in Math., Springer-Verlag, 1997. MR 99a:46034
  • [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. MR 94d:46012
  • [6] M. Fabian, G. Godefroy and V. Zizler, The structure of uniformly Gâteaux smooth Banach spaces, Israel J. Math. 124 (2001), 243-252. MR 2002g:46015
  • [7] M. Fabian, P. Habala, P. Hájek, V. Montesinos, J. Pelant and V. Zizler, Functional Analysis and infinite dimensional geometry, Canadian Math. Soc. Books, 8 (Springer-Verlag), 2001. MR 2002f:46001
  • [8] W. B. Johnson and J. Lindenstrauss, Some remarks on weakly compactly generated Banach spaces, Israel J. Math. 17 (1974), 219-230. MR 54:5808
  • [9] A. Moltó, J. Orihuela and S. Troyanski, Locally uniformly rotund renorming and fragmentability, Proc. London Math. Soc. (3) 75 (1997), 619-640. MR 98e:46011
  • [10] S. Negrepontis, Banach Spaces and Topology, Handbook of Set-Theoretic Topology (K. Kunen and J. Vaughan, eds.), North-Holland, 1984, pp. 1045-1142. MR 86i:46018
  • [11] M. Raja, Mesurabilité de Borel et renormages dans les espaces de Banach, (Doctoral dissertation), Printemps, 1998.
  • [12] J. Rychtár, Uniformly Gâteaux differentiable norms in spaces with unconditional basis, Serdica Math. J. 26 (2000), 353-358.MR 2003a:46025
  • [13] D. Yost, The Johnson-Lindenstrauss Space, Extracta Mathematicae 12 (1997), 185-192. MR 99a:46027
  • [14] V. Zizler, Nonseparable Banach spaces, Handbook on Banach spaces (W. B. Johnson and J. Lindenstrauss, eds.), to appear.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B03, 46E10

Retrieve articles in all journals with MSC (2000): 46B03, 46E10

Additional Information

Jan Rychtár
Affiliation: Department of Mathematical Analysis, Charles University, Faculty of Mathematics and Physics, Sokolovká 83, 186 75 Praha 8, Czech Republic
Address at time of publication: Department of Mathematics and Statistics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Keywords: Eberlein compacts, uniform rotundity in every direction
Received by editor(s): July 15, 2001
Published electronically: February 5, 2003
Additional Notes: Supported in part by GAČR 201/01/1198, A 1019003, NSERC 7926 and GAUK 277/2001. This paper is based on part of the author’s Ph.D. thesis written under the supervision of Professor V. Zizler
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2003 American Mathematical Society