SOME REMARKS ON THE SCHUR APPROXIMATION PROPERTY

Abstract

In this paper we study a modified version of the Schur approximation property recently introduced by J.A. de Reyna et. al. Our modification is along the lines of a compact approximation property that has been studied in the M-structure theory. We show that a space with the modified Schur approximation property has the hereditary Dunford and Pettis property and any subspace of it that is isomorphic to a dual space has the Schur property.