This is an announcement for the paper "A characterization of subspaces and quotients of reflexive Banach spaces with unconditional basis" by W. B. Johnson and Bentuo Zheng.

Abstract: We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. Then we prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a quotient of a reflexive Banach space with an unconditional finite dimensional decomposition embeds into a reflexive Banach space with an unconditional basis.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B03

The source file(s), JZh10.tex: 38045 bytes, is(are) stored in gzipped form as 0702199.gz with size 11kb. The corresponding postcript file has gzipped size 96kb.

Submitted from: btzheng@math.tamu.edu

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