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

2007/02/07 by Johnson, W. B., Zheng, Bentuo
#46B03 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/0702199

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.

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• A reflexive Banach space with an uncomplemented isometric subspace
• The cofinal property of the Reflexive Indecomposable Banach spaces
• Uniqueness of unconditional bases in Banach spaces
• A Banach space dichotomy for quotients of subspaces
• Subspace structure of some operator and Banach spaces