The $p$-Banach Saks property in symmetric operator spaces

Abstract

Let $E$ be a separable r.i. space which is an interpolation space between $L^{r}(\mathbb{R}^{+})$ and $L^{q}(\mathbb{R}^{+}),1<r<q<\infty$. We give sufficient conditions on $E$ implying that the symmetric operator space $E(\mathcal{M},\tau )$ has the $p$-Banach-Saks property for a suitable $p$, for an arbitrary semifinite von Neumann algebra $\mathcal{M}$.