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Incomparable, non isomorphic and minimal Banach spaces

Christian Rosendal
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Abstract

A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if $E_0$ does not reduce to isomorphism of the subspaces of a space, in particular, if the subspaces of the space admit a classification up to isomorphism by real numbers, then any subspace with an unconditional basis is isomorphic to its square and hyperplanes and has an isomorphically homogeneous subsequence.

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Christian Rosendal. 2004-07-07. Incomparable, non isomorphic and minimal Banach spaces. https://arxiv.org/abs/math/0407111

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