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ArticleOriginal scientific text

Title

σ-fragmented Banach spaces II

Authors 1, 2, 1

Affiliations

  1. Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England
  2. Department of Mathematics, GN-50, University of Washington, Seattle, Washington 98195, U.S.A.

Abstract

Recent papers have investigated the properties of σ-fragmented Banach spaces and have sought to find which Banach spaces are σ-fragmented and which are not. Banach spaces that have a norming M-basis are shown to be σ-fragmented using weakly closed sets. Zizler has shown that Banach spaces satisfying certain conditions have locally uniformly convex norms. Banach spaces that satisfy similar, but weaker conditions are shown to be σ-fragmented. An example, due to R. Pol, is given of a Banach space that is σ-fragmented using differences of weakly closed sets, but is not σ-fragmented using weakly closed sets.

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Studia Mathematica
1994/111/1
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Pages:
69-80
Main language of publication
English
Received
1993-10-21
Published
1994
Exact and natural sciences