This is an announcement for the paper "Non separable reflexive spaces admitting $\ell_1$ as a unique spreading model" by Spiros A. Argyros and Pavlos Motakis.

Abstract: Examples of non separable reflexive Banach spaces $\mathfrak{X}_{2^{\aleph_0}}$, admitting only $\ell_1$ as a spreading model, are presented. The definition of the spaces is based on $\alpha$-large, $\alpha<\omega_1$ compact families of finite subsets of the continuum. We show the existence of such families and we study their properties. Moreover, based on those families we construct a reflexive space $\mathfrak{X}_{2^{\aleph_0}}^\alpha$, $\alpha<\omega_1$ with density the continuum, such that every bounded non norm convergent sequence ${x_k}_k$ has a subsequence generating $\ell_1^\alpha$ as a spreading model.

Archive classification: math.FA math.CO

Mathematics Subject Classification: 46B03, 46B06, 46B26, 03E05

Remarks: 23 pages, no figures

Submitted from: pmotakis@central.ntua.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1302.0715

or

http://arXiv.org/abs/1302.0715