On the hereditary proximity to $\ell_1$

Spiros A. Argyros; Antonis Manoussakis; Anna M. Pelczar

paper

On the hereditary proximity to $ℓ_{1}$

arXiv:0907.4317

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 ξwe construct a separable reflexive space \mathfrak{X}_ξsuch that every infinite dimensional subspace of it has Bourgain \ell_1-index greater than ω^ξand the space itself has no \ell_1-spreading model. We also present a reflexive HI space admitting no \ell_p as a spreading model.

40 pages, submitted for publication, linguistic corrections

On the hereditary proximity to ℓ1​

Abstract

On the hereditary proximity to $ℓ_{1}$