Uniform Convexity and the Bishop-Phelps-Bollobas Property

Abstract

A new characterization of the uniform convexity of Banach space is obtained in the sense of the Bishop-Phelps-Bollobas theorem. It is also proved that the couple of Banach spaces (X, Y) has the Bishop-Phelps-Bollobas property for every Banach space Y when X is uniformly convex. As a corollary, we show that the Bishop-Phelps-Bollobas theorem holds for bilinear forms on l(p) x l(q) (1 < p,q <infinity).