The Bishop–Phelps–Bollobás theorem for operators (original) (raw)

We prove the Bishop-Phelps-Bollobás theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize those Banach spaces Y for which the Bishop-Phelps-Bollobás theorem holds for operators from 1 into Y . Several examples of classes of such spaces are provided. For instance, the Bishop-Phelps-Bollobás theorem holds when the range space is finite-dimensional, an L 1 (μ)-space for a σ -finite measure μ, a C(K)-space for a compact Hausdorff space K, or a uniformly convex Banach space. (R.M. Aron), domingo.garcia@uv.es (D. García), manuel.maestre@uv.es (M. Maestre).