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

S. Dilworth; Maria Girardi; Denka Kutzarova

Studia Mathematica (1995)

  • Volume: 112, Issue: 3, page 267-277
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Dilworth, S., Girardi, Maria, and Kutzarova, Denka. "Banach spaces which admit a norm with the uniform Kadec-Klee property." Studia Mathematica 112.3 (1995): 267-277. <http://eudml.org/doc/216153>.

@article{Dilworth1995,
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.},
author = {Dilworth, S., Girardi, Maria, Kutzarova, Denka},
journal = {Studia Mathematica},
keywords = {Kadec-Klee property; super-reflexive; renorming property for dual Banach spaces},
language = {eng},
number = {3},
pages = {267-277},
title = {Banach spaces which admit a norm with the uniform Kadec-Klee property},
url = {http://eudml.org/doc/216153},
volume = {112},
year = {1995},
}

TY - JOUR
AU - Dilworth, S.
AU - Girardi, Maria
AU - Kutzarova, Denka
TI - Banach spaces which admit a norm with the uniform Kadec-Klee property
JO - Studia Mathematica
PY - 1995
VL - 112
IS - 3
SP - 267
EP - 277
AB - 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.
LA - eng
KW - Kadec-Klee property; super-reflexive; renorming property for dual Banach spaces
UR - http://eudml.org/doc/216153
ER -

References

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