This is an announcement for the paper "On the hereditary proximity to $\ell_1$" by Spiros A. Argyros, A. Manoussakis, and Anna M. Pelczar.

Abstract: In the first part of the paper we present and discuss concepts of local and asymptotic hereditary proximity to \ell_1. The second part is devoted to a complete separation of the hereditary local proximity to \ell_1 from the asymptotic one. More precisely for every countable ordinal \xi we construct a separable reflexive space \mathfrak{X}_\xi such that every infinite dimensional subspace of it has Bourgain \ell_1-index greater than \omega^\xi and the space itself has no \ell_1-spreading model. We also present a reflexive HI space admitting no \ell_p as a spreading model.

Archive classification: math.FA

Mathematics Subject Classification: 46B20; 46B15; 03E10; 05A17

Remarks: 40 pages, submitted for publication

The source file(s), proximity.tex: 158273 bytes, is(are) stored in gzipped form as 0907.4317.gz with size 43kb. The corresponding postcript file has gzipped size 238kb.

Submitted from: anna.pelczar@im.uj.edu.pl

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