The weak Banach-Saks property for Hölder spaces

Abstract

We investigate the weak Banach--Saks property in the setting of Hölder spaces over metric spaces. We show that, for every infinite metric space $(M,d)$ and every $\alpha \in (0,1]$, the Hölder space $C^{\alpha }(M)$ fails to have the weak Banach--Saks property.