This is an announcement for the paper "Non-separable tree-like Banach spaces and Rosenthal's $\ell_1$-theorem " by Costas Poulios.

Abstract: We introduce and investigate a class of non-separable tree-like Banach spaces. As a consequence, we prove that we can not achieve a satisfactory extension of Rosenthal's $\ell_1$-theorem to spaces of the type $\ell_1(\kappa)$, for $\kappa$ an uncountable cardinal.

Archive classification: math.FA

Mathematics Subject Classification: 46B25, 46B26

Submitted from: k-poulios@math.uoa.gr

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

http://front.math.ucdavis.edu/1210.0792

or

http://arXiv.org/abs/1210.0792