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# On Locally Uniformly Rotund Renormings in C(K) Spaces

Published:2010-03-18
Printed: Jun 2010
• J. F. Martínez,
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, Valencia, Spain
• A. Moltó,
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, Valencia, Spain
• J. Orihuela,
Departamento de Matemáticas, Universidad de Murcia, Murcia, Spain
• S. Troyanski,
Departamento de Matemáticas, Universidad de Murcia, Murcia, Spain
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## Abstract

A characterization of the Banach spaces of type $C(K)$ that admit an equivalent locally uniformly rotund norm is obtained, and a method to apply it to concrete spaces is developed. As an application the existence of such renorming is deduced when $K$ is a Namioka--Phelps compact or for some particular class of Rosenthal compacta, results which were originally proved with \emph{ad hoc} methods.
 MSC Classifications: 46B03 - Isomorphic theory (including renorming) of Banach spaces 46B20 - Geometry and structure of normed linear spaces

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