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

Dilworth, S. ; Girardi, Maria ; Kutzarova, Denka

Studia Mathematica, Tome 113 (1995), p. 267-277 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $L_2(Ӿ)$ if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.

Détail

Publié le : 1995-01-01

Zbl 0824.46024

EUDML-ID : urn:eudml:doc:216153

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