On the continuity of biconjugate convex functions-Reference-Cited by-同舟云学术

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On the continuity of biconjugate convex functions

Published:2001-10-24 Issue:6 Volume:130 Page:1797-1803
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Borwein J.,Vanderwerff J.

Abstract

We show that a Banach space is a Grothendieck space if and only if every continuous convex function on X X has a continuous biconjugate function on X ∗ ∗ X^{**} , thus also answering a question raised by S. Simons. Related characterizations and examples are given.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2002-130-06/S0002-9939-01-06249-9/S0002-9939-01-06249-9.pdf

Reference13 articles.

1. On the convergence of subdifferentials of convex functions;Attouch, Hédy;Arch. Math. (Basel),1993

2. Characterizations of Banach spaces via convex and other locally Lipschitz functions;Borwein, J.;Acta Math. Vietnam.,1997

3. Examples of convex functions and classifications of normed spaces;Borwein, Jon;J. Convex Anal.,1994

4. Pitman Monographs and Surveys in Pure and Applied Mathematics;Deville, Robert,1993

5. Graduate Texts in Mathematics;Diestel, Joseph,1984

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