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1. A characterization of weakly compact sets by convex functions | |||
CHENG Qingjin | |||
Mathematics 20 January 2012 | |||
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Abstract:This note introduces a convexity property of convexfunctions defined on a nonempty convex set in Banach spaces and establishes several equivalent characterizations of weakcompactly subsets of Banach spaces by the property. More precisely, let X be a Banach space and let K∈X be a convex bounded subset. Then (i) If X is separable, then K is weakly compact iff thereexists a continuous 2R convex function on K.(ii) If X is nonseparable then K is weakly compact iffthere exists a continuous w2R convex function on K. | |||
TO cite this article:CHENG Qingjin. A characterization of weakly compact sets by convex functions[OL].[20 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4462252 |
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