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 ∞ to 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 ∞ ).