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@math.tamu.edu
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