Separable L-embedded Banach spaces are unique preduals

Hermann Pfitzner (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In this note the following is proved. Separable L-embedded spaces - that is separable Banach spaces which are complemented in their biduals such that the norm between the two complementary subspaces is additive - have property (X) which, by a result of Godefroy and Talagrand, entails uniqueness of the space as a predual.

Mots clés: L-embedded banach spaces; property (X); unique predual; copies of $c_0$

Domaines: Analyse fonctionnelle [math.FA]

Hermann Pfitzner. Separable L-embedded Banach spaces are unique preduals. Bull. Lond. Math. Soc., 2007, 39, pp.1039-1044. ⟨10.1112/blms/bdm077⟩. ⟨hal-00007545⟩