This is an announcement for the paper "Minimality, homogeneity and topological 0-1 laws for subspaces of a Banach space" by Valentin Ferenczi.

Abstract: If a Banach space is saturated with basic sequences whose linear span embeds into the linear span of any subsequence, then it contains a minimal subspace. It follows that any Banach space is either ergodic or contains a minimal subspace. If $X$ is a Banach space with a Schauder basis, the relation $E_0$ is Borel reducible to permutative equivalence between normalized block-sequences of $X$, or $X$ is $c_0$-saturated or $l_p$-saturated for some $1 \leq p <+\infty$. For a Banach space $X$ with an (unconditional) basis, topological 0-1 law type dichotomies are stated for block-subspaces of $X$ as well as for subspaces of $X$ with a successive FDD on its basis. A uniformity principle for properties of block-sequences, results about block-homogeneity, and a possible method to construct a Banach space with an unconditional basis, which has a complemented subspace without an unconditional basis, are deduced.

Archive classification: Functional Analysis; Combinatorics

Mathematics Subject Classification: 46B03; 46B15

The source file(s), ferenczitopolaw.tex: 93769 bytes, is(are) stored in gzipped form as 0502054.gz with size 26kb. The corresponding postcript file has gzipped size 99kb.

Submitted from: ferenczi@ccr.jussieu.fr

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http://arXiv.org/abs/math.FA/0502054

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