Weakly Lindelöf Determined Banach Space Projectional Resolution of the Identity Complemented Subspace Corson Compact Space Valdivia Compact Space
Issue Date:
2003
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 29, No 2, (2003), 95p-108p
Abstract:
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.
