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On the continuity of biconjugate convex functions

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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