THE BISHOP-PHELPS-BOLLOBAS PROPERTY FOR OPERATORS FROM L-infinity(mu) TO UNIFORMLY CONVEX BANACH SPACES

Abstract

Let X = L-infinity(mu) and Y be uniformly convex Banach space. We show that the pair (X, Y) has the Bishop-Phelps-Bollobas property for any measure space (Omega, mu). This solves a question raised by Acosta, Aron, Garcia, and Maestre. We also prove that if X is either complex L-infinity (mu) or complex c(0), and Y is complex uniformly convex, then the pair (X, Y) also has the Bishop-Phelps-Bollobas property.