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A dual differentiation space without an equivalent locally uniformly rotund norm
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 77 , Issue 3 , December 2004 , pp. 357 - 364
- Copyright
- Copyright © Australian Mathematical Society 2004
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