for suitable banach spaces $x$ and $y$ with schauder decompositions and a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$, it is shown that the strong banach-saks-ness of all evaluation operators on ${mathcal m}$ is a sufficient condition for the weak banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in y^*$, the evaluation op...