The strong Bishop-Phelps-Bollobás property

Abstract

In this paper we introduce the strong Bishop-Phelps-Bollobás property (sBPBp) for bounded linear operators between two Banach spaces $X$ and $Y$. This property is motivated by a Kim-Lee result which states, under our notation, that a Banach space $X$ is uniformly convex if and only if the pair $(X,\mathbb{K})$ satisfies the sBPBp. Positive results of pairs of Banach spaces $(X,Y)$ satisfying this property are given and concrete pairs of Banach spaces $(X,Y)$ failing it are exhibited. A complete characterization of the sBPBp for the pairs $({\ell }_p,{\ell }_q)$ is also provided.

17 pages, 1 figure

References in corpus (1)

• The Bishop-Phelps-Bollobás moduli of a Banach space