This is an announcement for the paper "Quantification of the Banach-Saks property" by Hana Bendova, Ondrej F.K. Kalenda and Jiri Spurny.

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 $\ell_1$-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 $\ell_1$-spreading models.

Archive classification: math.FA

Mathematics Subject Classification: 46B20

Remarks: 16 pages

Submitted from: kalenda@karlin.mff.cuni.cz

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

http://front.math.ucdavis.edu/1406.0684

or

http://arXiv.org/abs/1406.0684