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arXiv · 0907.4317

On the hereditary proximity to $\ell_1$

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

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Spiros A. Argyros, Antonis Manoussakis, Anna M. Pelczar. 2009-08-03. On the hereditary proximity to $\ell_1$. https://arxiv.org/abs/0907.4317

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