Note on distortion and Bourgain $\ell_1$ index

Details Note on distortion and Bourgain $\ell_1$ index Note on distortion and Bourgain $\ell_1$ index

2007-09-14

arxiv.org/abs/0709.2272v2

Mathematics

Functional Analysis

14 pages, remarks and references added

Scientific paper

The relation between different notions measuring proximity to $\ell_1$ and
distortability of a Banach space is studied. The main result states that a
Banach space, whose all subspaces have Bourgain $\ell_1$ index greater than
$\omega^\alpha$, $\alpha<\omega_1$, contains either an arbitrary distortable
subspace or an $\ell_1^\alpha$-asymptotic subspace.

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