Some remarks on farthest points

0358303 - MÚ 2012 RIV ES eng J - Journal Article
Montesinos, V. - Zizler, P. - Zizler, Václav
Some remarks on farthest points.
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Roč. 105, č. 1 (2011), s. 119-131. ISSN 1578-7303. E-ISSN 1579-1505
R&D Projects: GA AV ČR IAA100190901
Institutional research plan: CEZ:AV0Z10190503
Keywords : farthest points * strongly exposed points * generic differentiability * convex functions
Subject RIV: BA - General Mathematics
Impact factor: 0.340, year: 2011
http://link.springer.com/article/10.1007%2Fs13398-011-0012-z

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.
Permanent Link: http://hdl.handle.net/11104/0196390