ON THE p-SCHUR PROPERTY OF BANACH SPACES.

We introduce the notion of the p-Schur property (1≤p≤∞) 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. [ABSTRACT FROM AUTHOR]