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ArticleOriginal scientific text

Title

Valdivia compacta and equivalent norms

Authors 1

Affiliations

  1. Department of Mathematical Analysisi, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Abstract

We prove that the dual unit ball of a Banach space X is a Corson compactum provided that the dual unit ball with respect to every equivalent norm on X is a Valdivia compactum. As a corollary we show that the dual unit ball of a Banach space X of density ℵ1 is Corson if (and only if) X has a projectional resolution of the identity with respect to every equivalent norm. These results answer questions asked by M. Fabian, G. Godefroy and V. Zizler and yield a converse to Amir-Lindenstrauss' theorem.

Keywords

ENG
Corson compact space, Valdivia compact space, projectional resolution of the identity, countably 1-norming Markushevich basis, equivalent norm

Bibliography

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Studia Mathematica
2000/138/2
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Pages:
179-191
Main language of publication
English
Received
1999-03-15
Published
2000
Exact and natural sciences