On the hereditary proximity to $\ell_1$
Functional Analysis
2009-08-03 v2
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.
Keywords
Cite
@article{arxiv.0907.4317,
title = {On the hereditary proximity to $\ell_1$},
author = {Spiros A. Argyros and Antonis Manoussakis and Anna M. Pelczar},
journal= {arXiv preprint arXiv:0907.4317},
year = {2009}
}
Comments
40 pages, submitted for publication, linguistic corrections