Convex functions on Banach spaces not containing ℓ<sub>1</sub>

Title: Convex functions on Banach spaces not containing ℓ₁
Creator: Borwein, Jon; Vanderwerff, Jon
Relation: Canadian Mathematical Bulletin Vol. 40, Issue 1, p. 10-18
Publisher Link: http://dx.doi.org/10.4153/CMB-1997-002-1
Publisher: University of Toronto Press
Resource Type: journal article
Date: 1997
Description: 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.
Subject: convex functions; Banach spaces; differentiability properties; boundedness; convergence
Identifier: http://hdl.handle.net/1959.13/1046795
Identifier: uon:14688
Identifier: ISSN:0008-4395
Language: eng
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Convex functions on Banach spaces not containing ℓ1