A Characterization of Subspaces and Quotients of Reflexive Banach Spaces with Unconditional Bases

Details A Characterization of Subspaces and Quotients of Reflexive Banach Spaces with Unconditional Bases A Characterization of Subspaces and Quotients of Reflexive Banach Spaces with Unconditional Bases

2007-02-07

arxiv.org/abs/math/0702199v2

Mathematics

Functional Analysis

Scientific paper

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.

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