Duke Mathematical Journal

A characterization of subspaces and quotients of reflexive banach spaces with unconditional bases

W. B. Johnson and Bentuo Zheng

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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

Article information

Source
Duke Math. J., Volume 141, Number 3 (2008), 505-518.

Dates
First available in Project Euclid: 15 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1203087635

Digital Object Identifier
doi:10.1215/00127094-2007-003

Mathematical Reviews number (MathSciNet)
MR2387429

Zentralblatt MATH identifier
1146.46003

Subjects
Primary: 46B03: Isomorphic theory (including renorming) of Banach spaces
Secondary: 46B20: Geometry and structure of normed linear spaces

Citation

Johnson, W. B.; Zheng, Bentuo. A characterization of subspaces and quotients of reflexive banach spaces with unconditional bases. Duke Math. J. 141 (2008), no. 3, 505--518. doi:10.1215/00127094-2007-003. https://projecteuclid.org/euclid.dmj/1203087635


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