Uniform Convexity and the Bishop–Phelps–Bollobás Property

Abstract

AbstractA new characterization of the uniform convexity of Banach space is obtained in the sense of the Bishop–Phelps–Bollobás theorem. It is also proved that the couple of Banach spaces (X;Y) has the Bishop–Phelps–Bollobás property for every Banach space Y when X is uniformly convex. As a corollary, we show that the Bishop–Phelps–Bollobás theorem holds for bilinear forms on ℓp × ℓq (1 < p; q < ∞).