Bulletin of the Australian Mathematical Society

Table of Contents - 1991 - Volume 43, Issue 01  

Research Article

A factor theorem for locally convex differentiability spaces

Roger Eylanda1 and Bernice Sharpa2

a1 Department of Pure Mathematics, University of Sydney, New South Wales 2006, Australia

a2 Australian Catholic University, 40 Edward Street North Sydney NSW 2060, Australia

Abstract

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.

(Received February 15 1990)

--