[Banach] Abstract of a paper by W. B. Johnson and Bentuo Zheng

[Dale Alspach]

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 at 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 at arXiv.org.