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A dual differentiation space without an equivalent locally uniformly rotund norm

Published online by Cambridge University Press:  09 April 2009

Petar S. Kenderov
Affiliation:
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria e-mail: [email protected]
Warren B. Moors
Affiliation:
Department of Mathematics, The University of Auckland, Auckland, New Zealand e-mail: [email protected]
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Abstract

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A Banach space (X, ∥ · ∥) is said to be a dual differentiation space if every continuous convex function defined on a non-empty open convex subset A of X* that possesses weak* continuous subgradients at the points of a residual subset of A is Fréchet differentiable on a dense subset of A. In this paper we show that if we assume the continuum hypothesis then there exists a dual differentiation space that does not admit an equivalent locally uniformly rotund norm.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

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