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On Locally Uniformly Rotund Renormings in C(K) Spaces

Published online by Cambridge University Press:  20 November 2018

J. F. Martínez ,
A. Moltó ,
J. Orihuela  and
S. Troyanski
J. F. Martínez
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, Valencia, Spain, e-mail: j.francisco.martinez@uv.es, anibal.molto@uv.es
A. Moltó
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Murcia, Spain, e-mail: joseori@um.es, stroya@um.es
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Abstract

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A characterization of the Banach spaces of type $C\left( K \right)$ 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 ad hoc methods.

Keywords

46B0346B20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 3 , 01 June 2010 , pp. 595 - 613
Copyright
Copyright © Canadian Mathematical Society 2010

References

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