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On the characterisation of Asplund spaces

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

Published online by Cambridge University Press:  09 April 2009

J. R. Giles
J. R. Giles
Affiliation:
University of Newcastle, Newcastle, N.S.W. 2308, Australia
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Abstract

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A Banach space is an Asplund space if every continuous convex function on an open convex subset is Fréchet differentiable on a dense G8 subset of its domain. The recent research on the Radon-Nikodým property in Banach spaces has revealed that a Banach space is an Asplund space if and only if every separable subspace has separable dual. It would appear that there is a case for providing a more direct proof of this characterisation.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces 46B22: Radon-Nikodým, Kreĭn-Milman and related properties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 1 , January 1982 , pp. 134 - 144
Copyright
Copyright © Australian Mathematical Society 1982

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