An extension property for banach spaces

Abstract

A Banach space X has property (E) if every operator from X into c0 extends to an operator from X** into c0; X has property (L) if whenever K ⊆ X is limited in X**, then K is limited in X; X has property (G) if whenever K ⊆ X is Grothendieck in X**, then K is Grothendieck in X. In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips properties, and the property of being a Grothendieck space. © 2002, Instytut Matematyczny. All rights reserved.