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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
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Abstract

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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