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arXiv · 1104.3543

$\alpha$-minimal Banach spaces

Christian Rosendal
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Abstract

A Banach space with a Schauder basis is said to be $\alpha$-minimal for some countable ordinal $\alpha$ if, for any two block subspaces, the Bourgain embeddability index of one into the other is at least $\alpha$. We prove a dichotomy that characterises when a Banach space has an $\alpha$-minimal subspace, which contributes to the ongoing project, initiated by W. T. Gowers, of classifying separable Banach spaces by identifying characteristic subspaces.

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Christian Rosendal. 2011-04-18. $\alpha$-minimal Banach spaces. https://arxiv.org/abs/1104.3543

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