On the continuity of biconjugate convex functions
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- by J. M. Borwein and J. D. Vanderwerff PDF
- Proc. Amer. Math. Soc. 130 (2002), 1797-1803 Request permission
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.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
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1797-1803
- MSC (2000): Primary 46B20, 52A41
- DOI: https://doi.org/10.1090/S0002-9939-01-06249-9
- MathSciNet review: 1887028