Non-separable tree-like Banach spaces and Rosenthal's $\ell _{1}$-theorem
Volume 221 / 2014
Studia Mathematica 221 (2014), 1-12
MSC: Primary 46B25, 46B26.
DOI: 10.4064/sm221-1-1
Abstract
We introduce and investigate a class of non-separable tree-like Banach spaces. As a consequence, we prove that we cannot achieve a satisfactory extension of Rosenthal's $\ell _1$-theorem to spaces of the type $\ell _1(\kappa )$ for $\kappa $ an uncountable cardinal.
