On the p-Schur property of Banach spaces

Abstract

We introduce the notion of the $p$-Schur property ($1\le p\le \infty$) as a generalization of the Schur property of Banach spaces, and then we present a number of basic properties and some examples. We also study its relation with some geometric properties of Banach spaces, such as the Gelfand–Phillips property. Moreover, we verify some necessary and sufficient conditions for the $p$-Schur property of some closed subspaces of operator spaces.