Borwein, Jonathan M. and Vanderwerff, Jon D. (2000) On the continuity of biconjugate convex functions. Proceedings of the American Mathematical Society, 30 (6). pp. 1797-1803. ISSN 0002-9939
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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.
| Item Type: | Article |
|---|---|
| Additional Information: | pubdom FALSE |
| Uncontrolled Keywords: | continuous convex function, conjugate function, Grothendieck space |
| Subjects: | 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories 46-xx Functional analysis > 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) 46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices 52-xx Convex and discrete geometry > 52Axx General convexity |
| Faculty: | UNSPECIFIED |
| Depositing User: | Users 1 not found. |
| Date Deposited: | 28 Nov 2003 |
| Last Modified: | 13 Jan 2015 11:57 |
| URI: | https://docserver.carma.newcastle.edu.au/id/eprint/230 |
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