Compact convex sets that admit a lower semicontinuous strictly convex function

L. García-Lirola; J. Orihuela; M. Raja

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arXiv · 1510.07921

Compact convex sets that admit a lower semicontinuous strictly convex function

L. García-Lirola·J. Orihuela·M. Raja

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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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BibTeX RIS

L. García-Lirola, J. Orihuela, M. Raja. 2015-10-27. Compact convex sets that admit a lower semicontinuous strictly convex function. https://arxiv.org/abs/1510.07921

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