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Convex functions on Banach spaces not containing ℓ1

Published online by Cambridge University Press:  20 November 2018

Jon Borwein  and
Jon Vanderwerff
Jon Borwein
Affiliation:
Department of Mathematics & Statistics Simon Fraser University Burnaby, BC V5A 1S6, e-mail: jborwein@cs.sfu.ca
Jon Vanderwerff
Affiliation:
Department of Mathematics Walla Walla College College Place, WA USA 99324, e-mail: vandjo@wwc.edu
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Abstract

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There is a sizeable class of results precisely relating boundedness, convergence and differentiability properties of continuous convex functions on Banach spaces to whether or not the space contains an isomorphic copy of ℓ1. In this note, we provide constructions showing that the main such results do not extend to natural broader classes of functions.

Keywords

46A5546B2052A41
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 1 , 01 March 1997 , pp. 10 - 18
Copyright
Copyright © Canadian Mathematical Society 1997

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