The phillips properties

Abstract

A Banach space X has the Phillips property if the canonical projection p: X*** → X* is sequentially weak*-norm continuous, and has the weak Phillips property if p is sequentially weak*-weak continuous. We study both properties in connection with other geometric properties, such as the Dunford-Pettis property, Pelczynski's properties (u) and (V), and the Schur property. © 2000 by Walden Freedman and Ali Ülger.