This is an announcement for the paper "Incomparable, non isomorphic and minimal Banach spaces" by Christian Rosendal.

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.

Archive classification: Functional Analysis; Logic

The source file(s), ArchiveIncomparable.tex: 57150 bytes, is(are) stored in gzipped form as 0407111.gz with size 19kb. The corresponding postcript file has gzipped size 81kb.

Submitted from: rosendal@ccr.jussieu.fr

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http://front.math.ucdavis.edu/math.FA/0407111

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http://arXiv.org/abs/math.FA/0407111

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