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Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1699

Title: A Characterization of Weakly Lindelöf Determined Banach Spaces
Authors: Kalenda, Ondřej
Keywords: 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.
Description: 2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.
URI: http://hdl.handle.net/10525/1699
ISSN: 1310-6600
Appears in Collections:Volume 29 Number 2

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