Quantification of the Banach-Saks property
arXiv:1406.0684 · doi:10.1016/j.jfa.2014.12.003
Abstract
We investigate possible quantifications of the Banach-Saks property and the weak Banach-Saks property. We prove quantitative versions of relationships of the Banach-Saks property of a set with norm compactness and weak compactness. We further establish a quantitative version of the characterization of the weak Banach-Saks property of a set using uniform weak convergence and -spreading models. We also study the case of the unit ball and in this case we prove a dichotomy which is an analogue of the James distortion theorem for -spreading models.
18 pages; we added some references to related results, remarks on this relationship, the proof of one lemma was simplified