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Locally uniformly rotund renorming and fragmentability

Published online by Cambridge University Press:  01 November 1997

A Moltó ,
J Orihuela  and
S Troyanski
A Moltó
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, Dr. Moliner 50, 46100 Burjassot (Valencia), Spain
J Orihuela
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain
S Troyanski
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, Dr. Moliner 50, 46100 Burjassot (Valencia), Spain Faculty of Mathematics and Informatics, Sofia University, 5, James Bourchier Blvd. 1126 Sofia, Bulgaria
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Abstract

In this paper we characterize those Banach spaces $E$ that admit a locally uniformly rotund renorming by means of a linear topological condition that is a particular case of the notion, introduced by J. E. Jayne, I. Namioka and C. A. Rogers, called countable cover by sets of small local diameter. This allows us to develop a Decomposition Method and a Transfer Technique to obtain locally uniformly rotund renormings.

1991 Mathematics Subject Classification: 46B20.

Keywords

locally uniformly rotund$\sigma$-fragmentabilitycountable cover by sets of small local diameter slicetransfer techniquethree space problem
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 75 , Issue 3 , November 1997 , pp. 619 - 640
Copyright
London Mathematical Society 1997

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