A NONLINEAR BISHOP-PHELPS-BOLLOBAS TYPE THEOREM

Abstract

The main aim of this paper is to prove a Bishop-Phelps-Bollobas type theorem on the unital uniform algebra A(w*u)(B-X*) consisting of all w*-uniformly continuous functions on the closed unit ball B-X* which are holomorphic on the interior of B-X*. We show that this result holds for A(w*u)(B-X*) if X* is uniformly convex or X* is the uniformly complex convex dual space of an order continuous absolute normed space. The vector-valued case is also studied. Throughout the paper, we consider complex Banach spaces.