Weakly Lindelöf Determined Banach Space Projectional Resolution of the Identity Complemented Subspace Corson Compact Space Valdivia Compact Space
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 29, No 2, (2003), 95p-108p
We prove that a Banach space X is weakly Lindelöf determined if (and only if) each non-separable Banach space isomorphic to a
complemented subspace of X has a projectional resolution of the identity.
This answers a question posed by S. Mercourakis and S. Negrepontis and yields a converse of Amir-Lindenstrauss’ theorem. We also prove that a Banach space of the form C(K) where K is a continuous image of a Valdivia compactum is weakly Lindelöf determined if (and only if) each non-separable Banach space isometric to a subspace of C(K) has a projectional resolution of the identity.