A separable L-embedded Banach space has property (X) and is therefore the unique predual of its dual

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75816In 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.Functional Analysis46B04, 46B03, 46B20A separable L-embedded Banach space has property (X) and is therefore the unique predual of its dualtext