Compact convex sets that admit a lower semicontinuous strictly convex function

2015/10/27 by Luis C. García‐Lirola, García-Lirola, L., J. Orihuela +3
Mathematics · Computer Science · #Advanced Banach Space Theory #Optimization and Variational Analysis #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.1510.07921

Abstract

We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with its weak^* topology. In addition, we find exposed points where a strictly convex lower semicontinuous function is continuous.

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