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 SpaceProjectional Resolution of the IdentityComplemented SubspaceCorson Compact SpaceValdivia 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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