This is an announcement for the paper "Compact convex sets that admit a lower semicontinuous strictly convex function" by L. Garcia-Lirola, J. Orihuela, and M. Raja.
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.
Archive classification: math.FA
Mathematics Subject Classification: 46A55 (Primary) 46B03, 54E35 (Secondary)
Remarks: 9 pages
Submitted from: luiscarlos.garcia@um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.07921
or