The Bishop-Phelps-Bollobas theorem for operators on L-1(mu)

Abstract

In this paper we show that the Bishop-Phelps-Bollobas theorem holds for L(L-1(mu), L-1(v)) for all measures and v and also holds for L(L-1(mu), L-infinity(nu)) for every arbitrary measure mu and every localizable measure nu Finally, we show that the Bishop-Phelps-Bollobas theorem holds for two classes of bounded linear operators from a real L-1(mu) into a real C(K) if mu is a finite measure and K is a compact Hausdorff space. In particular, one of the classes includes all Bochner representable operators and all weakly compact operators. (c) 2014 Elsevier Inc. All rights reserved.