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On uniformly Gâteaux differentiable norms in C(K)

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

A. Moltó  and
S. Troyanski
A. Moltó
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, Dr. Moliner 50, 46100-Burjasot (Valencia), Spain.
S. Troyanski
Affiliation:
Department of Mathematics and Informatics, Sofia University, 5, James Bourchier Blvd., 1126 Sofia, Bulgaria.
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Abstract

It is proved that C(K) has no equivalent uniformly Gâteaux differentiable norm (UGD) when K-is an uncountable separable scattered com¬pact space. This result is applied to obtain an example of scattered compact K such that K′″ = ∅ and C(K) has no UGD renorming.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 233 - 238
Copyright
Copyright © University College London 1994

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