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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.

Abstract.A Banach space X has property (E) if every operator from X into c 0 extends to an operator from X * * into c 0 ; X has property (L) if whenever K ⊆ X is limited in X

No abstract