Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T05:14:15.066Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Space With no Locally Uniformly Rotund Renorming

Published online by Cambridge University Press:  20 November 2018

Richard Haydon  and
Vaclav Zizler
Richard Haydon
Affiliation:
Brasenose College, Oxford, England
Vaclav Zizler
Affiliation:
University of Alberta, Edmonton, Alberta, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct a Banach space X which has no equivalent (wLUR) norm but which has no subspace isomorphic to l∞.

Keywords

46B20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 122 - 128
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Haydon, R. G., A non-reflexive Grothendieck space which does not contain l∞ , Israel J. Math. 40 (1981), 65-73.Google Scholar
2. , An unconditional result about Grothendieck spaces, Proc. Amer. Math. Soc. 100 (1987), 511–516. Google Scholar
3. , Levy, M. F. and Odell, E., On sequences without weak* convergent convex block subsequences, Proc. Amer. Math. Soc. 100 (1987), 94–98. Google Scholar
4. Lindenstrauss, J., Weakly compact sets - their topological properties and the Banach spaces they generate, Ann. of Math. Studies, 69 (1972), 235–273. Google Scholar
5. Talagrand, M., Un nouveau C﹛K) qui possède la propriété de Grothendieck, Israel J. Math., 37 (1980), 181–191. Google Scholar