Compact convex sets that admit a lower semicontinuous strictly convex function
Functional Analysis
2015-10-28 v1
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.
Keywords
Cite
@article{arxiv.1510.07921,
title = {Compact convex sets that admit a lower semicontinuous strictly convex function},
author = {L. García-Lirola and J. Orihuela and M. Raja},
journal= {arXiv preprint arXiv:1510.07921},
year = {2015}
}
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9 pages