Abstract of a paper by W. B. Johnson and Bentuo Zheng
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0702199 or http://arXiv.org/abs/math.FA/0702199 or by email in unzipped form by transmitting an empty message with subject line uget 0702199 or in gzipped form by using subject line get 0702199 to: math@arXiv.org.
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Dale Alspach