L-embedded Banach spaces and a weak version of Phillips lemma

Hermann Pfitzner (1)

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

After a short survey on L-embedded Banach spaces - for which Bochner spaces of the form L1(X) with re exive X serve as examples - we prove that these spaces satisfy a weak form of Phillips' lemma: It is proved that the L-projection of an L-embedded Banach spaces sends relatively w- sequentially compact sets to relatively weakly sequentially compact sets.

Domaines: Analyse fonctionnelle [math.FA]

Hermann Pfitzner. L-embedded Banach spaces and a weak version of Phillips lemma. Vector Measures, Integration and Applications, Sep 2008, Eichstätt, Germany. pp.339-344. ⟨hal-00463783⟩