Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T05:23:08.347Z Has data issue: false hasContentIssue false
  • English
  • Français

A new Banach space without the Kadec-Klee property

Published online by Cambridge University Press:  17 April 2009

G.A. Alexandrov  and
V.D. Babev
G.A. Alexandrov
Affiliation:
Department of MathematicsUniversity of SofiaSofiaBulgaria
V.D. Babev
Affiliation:
Department of MathematicsUniversity of SofiaSofiaBulgaria
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.

An example of a Banach space is given which does not contain isomorphically l1 and does not admit the Kadec-Klee property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 3 , June 1992 , pp. 463 - 465
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Alexandrov, G.A., ‘Banach spaces without Kadec-Klee property’, Canad. Math. Bull. (to appear).Google Scholar
[2]Haydon, R., ‘A non-reflexive Grothendieck space which does not contain l ∞’, Israel J. Math. 40 (1981), 65–73.CrossRefGoogle Scholar
[3]Haydon, R., ‘A counterexample to several questions about scattered compact spaces’, (preprint).Google Scholar
[4]Troyanski, S.L., ‘On the equivalent norms and minimal systems in non-separable Banach spaces’, Studia Math. 43 (1972), 125–138.Google Scholar