Banach spaces which admit a norm with the uniform Kadec-Klee property
Volume 112 / 1995
Studia Mathematica 112 (1995), 267-277
DOI: 10.4064/sm-112-3-267-277
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 $L_2(Ӿ)$ if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.
