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Convex functions on Banach spaces not containing ℓ1
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Research Article
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- Copyright © Canadian Mathematical Society 1997
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