A Bishop-Phelps-Bollobás theorem for bounded analytic functions

Abstract

Let H∞ denote the Banach algebra of all bounded analytic functions on the open unit disc and denote by B(H∞) the Banach space of all bounded linear operators from H∞ into itself. We prove that the Bishop-Phelps-Bollobás property holds for B(H∞). As an application to our approach, we prove that the Bishop-Phelps-Bollobás property also holds for operator ideals of B(H∞).