Bishop-Phelps-Bollobás Theorem and Properties for Operators and Approximate Hyperplane Series

Abstract

The Lindelöf property and Bishop-Phelps-Bollobás moduli in Banach spaces are studied. The Bishop-Phelps-Bollobás theorem for operators from c_0 to uniformly convex spaces, for bilinear forms and for uniform algebras are established. We characterize the Bishop-Phelps-Bollobás property for numerical radius in l_1 (C) operators on C(K), for certain spaces of operators and for numerical radius of operators on L_1 (μ). Asplund operators, Γ-flatness and Bishop–Phelps–Bollobás type theorems for operators, version of Lindenstrauss properties A and B and approximation hyperplane series properties are considered.