[Banach] Abstract of a paper by W. B. Johnson and Bentuo Zheng
alspach at www.math.okstate.edu
Thu Feb 8 12:46:40 CST 2007
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
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Submitted from: btzheng at math.tamu.edu
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