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On strongly exposing functionals

Published online by Cambridge University Press:  09 April 2009

Ka-Sing Lau
Ka-Sing Lau
Affiliation:
University of Pittsburgh, Pittsburgh, Pa. 15260, U.S.A.
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Abstract

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Let X be a real Banach space and let K be a bounded closed convex subset of X. We prove that the set of strongly exposing functions K^ of K is a (norm) dense G8 in X* if and only if for any bounded closed convex subset C such that K⊄C, there exists a point x in K which is a strongly exposed point of conv (C ∪ K). As an application, we show that if X* is weakly compact generated, then for any weakly compact subset K in X, the set K^ is a dense G8 in X*.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 3 , May 1976 , pp. 362 - 367
Copyright
Copyright © Australian Mathematical Society 1976

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