%0 Journal Article
%T On the hereditary proximity to $\ell_1$
%A Spiros A. Argyros
%A Antonis Manoussakis
%A Anna M. Pelczar
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0907.4317v2