A Characterization of Subspaces and Quotients of Reflexive Banach Spaces with Unconditional Bases
Functional Analysis
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0702199,
title = {A Characterization of Subspaces and Quotients of Reflexive Banach Spaces with Unconditional Bases},
author = {W. B. Johnson and Bentuo Zheng},
journal= {arXiv preprint arXiv:math/0702199},
year = {2007}
}