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A factor theorem for locally convex differentiability spaces

Published online by Cambridge University Press:  17 April 2009

Roger Eyland  and
Bernice Sharp
Roger Eyland
Affiliation:
Department of Pure Mathematics, University of Sydney, New South Wales 2006, Australia
Bernice Sharp
Affiliation:
Australian Catholic University, 40 Edward Street North Sydney NSW 2060, Australia
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Abstract

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The main result of this paper is that a continuous convex function with domain in a locally convex space factors through a normed space. In a recent paper by Sharp, topological linear spaces are categorised according to the differentiability properties of their continuous convex functions; we show that under suitable conditions the classification is preserved by linear maps. A technique for deducing results for locally convex spaces from Banach space theory is an immediate consequence. Examples are given and Asplund C(S) spaces are characterised.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 1 , February 1991 , pp. 101 - 113
Copyright
Copyright © Australian Mathematical Society 1991

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