Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Prof. Cheng Lixin,Xiamen University
Analytic characterizations of Mazur's intersection property via convex functions
A Banach space X has Mazur's intersection property (MIP) provided every bounded closed convex set of it can be represented as an intersection of closed balls. In this talk, making use of the Br?ndsted-Rockafellar theorem and a minimax theorem of Ky-Fan type, we show that a sufficient and necessary condition for X admitting the MIP is for every enxtended-real-valued lower semi -continuous convex function f on X there exists a family G of convex functions of the form: ，if ；otherwise such that and that X has the CIP (for the property that every compact convex set is an intersection of closed balls) if and only if for every continuous convex Lipschitz function f on X* there exists a family H of convex functions of the form: for all such that.
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