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Displaying similar documents to “Some open problems on functional analysis and function theory.”

A converse to Amir-Lindenstrauss theorem in complex Banach spaces.

Ondrej F. K. Kalenda (2006)

RACSAM

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We show that a complex Banach space is weakly Lindelöf determined if and only if the dual unit ball of any equivalent norm is weak* Valdivia compactum. We deduce that a complex Banach space X is weakly Lindelöf determined if and only if any nonseparable Banach space isomorphic to a complemented subspace of X admits a projectional resolution of the identity. These results complete the previous ones on real spaces.

A survey on the Szlenk index and some of its applications.

Gilles Lancien (2006)

RACSAM

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We describe how the Szlenk index has been used in various areas of the geometry of Banach spaces. We cover the following domains of application of this notion: non existence of universal spaces, linear classification of C(K) spaces, descriptive set theory, renorming problems and non linear classification of Banach spaces.

A Characterization of Weakly Lindelöf Determined Banach Spaces

Kalenda, Ondřej (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 46B26, 46B03, 46B04. 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...