Abstract
We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property (UTP) has the UTP. This is used to prove that a separable reflexive Banach space with the UTP embeds into a reflexive Banach space with an unconditional basis. This solves several longstanding open problems. In particular, it yields that a quotient of a reflexive Banach space with an unconditional finite-dimensional decomposition (UFDD) embeds into a reflexive Banach space with an unconditional basis
Citation
W. B. Johnson. Bentuo Zheng. "A characterization of subspaces and quotients of reflexive banach spaces with unconditional bases." Duke Math. J. 141 (3) 505 - 518, 15 February 2008. https://doi.org/10.1215/00127094-2007-003
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