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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the continuity of biconjugate convex functions


Authors: J. M. Borwein and J. D. Vanderwerff
Journal: Proc. Amer. Math. Soc. 130 (2002), 1797-1803
MSC (2000): Primary 46B20, 52A41
Published electronically: October 24, 2001
MathSciNet review: 1887028
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Abstract: We show that a Banach space is a Grothendieck space if and only if every continuous convex function on $X$ has a continuous biconjugate function on $X^{**}$, thus also answering a question raised by S. Simons. Related characterizations and examples are given.


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Additional Information

J. M. Borwein
Affiliation: Department of Mathematics & Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email: jborwein@cecm.sfu.ca

J. D. Vanderwerff
Affiliation: Department of Mathematics, La Sierra University, Riverside, California 92515
Email: jvanderw@lasierra.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06249-9
PII: S 0002-9939(01)06249-9
Keywords: Continuous convex function, conjugate function, Grothendieck space
Received by editor(s): September 11, 2000
Received by editor(s) in revised form: January 9, 2001
Published electronically: October 24, 2001
Additional Notes: The first author’s research was supported by an NSERC grant
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2001 American Mathematical Society