Quantification of the Banach-Saks property
  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. 
Hana Bendov\'a, Ond\v{r}ej F.K. Kalenda and Ji\v{r}\'i Spurn\'y
math.FA