Some remarks on farthest points

Autores UPV
Revista Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas


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. © 2011 Springer-Verlag.