Kadec norms and Borel sets in a Banach space

M. Raja

ArticleOriginal scientific text

Title

Kadec norms and Borel sets in a Banach space

Authors ¹

Affiliations

Mathématiques Pures, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence Cedex, France

Abstract

We introduce a property for a couple of topologies that allows us to give simple proofs of some classic results about Borel sets in Banach spaces by Edgar, Schachermayer and Talagrand as well as some new results. We characterize the existence of Kadec type renormings in the spirit of the new results for LUR spaces by Moltó, Orihuela and Troyanski.

Keywords

ENG

Borel sets, Countable cover by sets of local small diameter, Kadec renorming, Radon-Nikodym compact spaces

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Title

Kadec norms and Borel sets in a Banach space

Affiliations

Abstract

Keywords

Bibliography