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Title

Banach spaces which admit a norm with the uniform Kadec-Klee property

Authors 1, 1, 2

Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, U.S.A.
  2. Institute of Mathematics, Bulgarian Academy of Sciences, 1090 Sofia, Bulgaria.

Abstract

Several results are established about Banach spaces Ӿ which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from Ӿ to the Lebesgue-Bochner space L2(Ӿ) if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.

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Studia Mathematica
1994-1995/112/3
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Pages:
267-277
Main language of publication
English
Received
1993-10-21
Accepted
1994-05-12
Published
1995
Exact and natural sciences