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A CONTINUITY CHARACTERIZATION OF ASPLUND SPACES

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

Published online by Cambridge University Press:  07 February 2011

J. R. GILES
J. R. GILES*
Affiliation:
School of Mathematical and Physical Sciences, The University of Newcastle, New South Wales 2308, Australia (email: John.Giles@newcastle.edu.au)
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Abstract

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A Banach space is an Asplund space if every continuous gauge has a point where the subdifferential mapping is Hausdorff weak upper semi-continuous with weakly compact image. This contributes towards the solution of a problem posed by Godefroy, Montesinos and Zizler.

Keywords

Fréchet differentiabilitysubdifferential mappingweak upper semi-continuitygaugeextreme pointpolarRadon–Nikodým property

MSC classification

Secondary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 3 , June 2011 , pp. 450 - 455
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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