On the continuity of biconjugate convex functions

Borwein, J.; Vanderwerff, J.

doi:10.1090/S0002-9939-01-06249-9

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.

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