On Banach spaces which are M-ideals in their biduals

Resumen

A Banach space X is an M-ideal in its bidual if the relation ||f + w|| = ||f|| + ||w|| holds for every f in X* and every w in X ^. The class of the Banach spaces which are M-ideals in their biduals, in short, the class of M-embedded spaces, has been carefully investigated, in particular by A. Lima, G. Godefroy and the West Berlin School. The spaces c0(I) -I any set- equipped with their canonical norm belong to this class, which also contains e.g. certain spaces K(E,F) of compact operators between reflexive spaces (see [7]). This class has very nice properties; for instance, these are Weakly Compactly Generated (W.C.G.) Asplund spaces [2; Th. 3], have the property (v) [5; Th. 1] and (u) [4; Main Th.] of Pelczynski and satisfy, among other isometric properties, that every isometric isomorphism of X** is the bitranspose of an isometric isomorphism of X [6; Prop. 4.2]. The purpose of this work is to show that these properties are also true in a wider class of Banach spaces