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15 February 2008 A characterization of subspaces and quotients of reflexive banach spaces with unconditional bases
W. B. Johnson, Bentuo Zheng
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Duke Math. J. 141(3): 505-518 (15 February 2008). DOI: 10.1215/00127094-2007-003

Abstract

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property (UTP) has the UTP. This is used to prove that a separable reflexive Banach space with the UTP embeds into a reflexive Banach space with an unconditional basis. This solves several longstanding open problems. In particular, it yields that a quotient of a reflexive Banach space with an unconditional finite-dimensional decomposition (UFDD) embeds into a reflexive Banach space with an unconditional basis

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W. B. Johnson. Bentuo Zheng. "A characterization of subspaces and quotients of reflexive banach spaces with unconditional bases." Duke Math. J. 141 (3) 505 - 518, 15 February 2008. https://doi.org/10.1215/00127094-2007-003

Information

Published: 15 February 2008
First available in Project Euclid: 15 February 2008

zbMATH: 1146.46003
MathSciNet: MR2387429
Digital Object Identifier: 10.1215/00127094-2007-003

Subjects:
Primary: 46B03
Secondary: 46B20

Rights: Copyright © 2008 Duke University Press

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Vol.141 • No. 3 • 15 February 2008
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