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Analytic characterizations of Mazur's intersection property via convex functions

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Analytic characterizations of Mazur's intersection property via convex functions.htm (413bytes)
Date
2012-06
Author
Chen, Lizhen
Cheng, Lixin
程立新
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  • 数学科学-已发表论文 [2662]
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Abstract
In this paper, we present analytical characterizations of Mazur's intersection property (MIP), the CIP and the MIP* via a specific class of convex functions and their conjugates. More precisely, let X be a Banach space and X* be its dual. Then X has the MIP if and only if for every extended real-valued lower semi-continuous convex function f defined on X with bounded domain, f is the supremum of all functions g <= f of the form: g(x) = r(0) - root R-2 - parallel to x - x(0)parallel to(2), if parallel to x - x(0)parallel to <= R; = + infinity, otherwise for some x(0) is an element of X (X*) and r(0) is an element of R, R > 0. And X has the CIP if and only if for every extended real-valued lower semi-continuous convex function on X with relatively compact domain, f* is the infimum of all functions h >= f* which are of the form: h(x*) = R-0 root 1 + parallel to x*parallel to(2) + (x*, x(0)) + r(0), for all x* is an element of X*. (C) 2012 Elsevier Inc. All rights reserved.
Citation
JOURNAL OF FUNCTIONAL ANALYSIS,2012,262(11):4731-4745
URI
http://dx.doi.org/10.1016/j.jfa.2012.03.014
WOS:000303087000004
https://dspace.xmu.edu.cn/handle/2288/15429

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