Abstract
We use renormings and generic differentiability of convex functions to prove some results on farthest points in sets in Banach spaces. As a corollary, we obtain an alternative proof of the Lindenstrauss–Troyanski result on representation of weakly compact convex sets by means of strongly exposed points. We use this approach to simplify former proofs of several known results in this area.
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V. Montesinos’s work was supported in part by Proyecto MTM2008-03211. Ministerio de Ciencia e Innovación, by a Grant BEST 2010-134 of the Generalitat Valenciana, and by a Grant from the Universidad Politécnica de Valencia, PAID 2009, Spain.
P. Zizler thanks Mount Royal University, Calgary, Canada, for its support.
V. Zizler’s work was supported in part by a Grant AVOZ 101 905 03 and IAA 100190901 (Czech Republic).
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Montesinos, V., Zizler, P. & Zizler, V. Some remarks on farthest points. RACSAM 105, 119–131 (2011). https://doi.org/10.1007/s13398-011-0012-z
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DOI: https://doi.org/10.1007/s13398-011-0012-z