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On the continuity of biconjugate convex functions
Author(s):
J.
M.
Borwein;
J.
D.
Vanderwerff
Journal:
Proc. Amer. Math. Soc.
130
(2002),
1797-1803.
MSC (2000):
Primary 46B20, 52A41
Posted:
October 24, 2001
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Abstract:
We show that a Banach space is a Grothendieck space if and only if every continuous convex function on  has a continuous biconjugate function on  , thus also answering a question raised by S. Simons. Related characterizations and examples are given.
References:
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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:
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
Posted:
October 24, 2001
Additional Notes:
The first author's research was supported by an NSERC grant
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2001,
American Mathematical Society
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