Weak Banach-Saks property in the space of compact operators

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 $x\in X$ and $y^*\in‎ ‎Y^*$‎, ‎the evaluation operators on $\mathcal{M}$ are defined by‎ ‎$\phi_x(T)= Tx$ and $\psi_{y^*}(T)= T^*y^*.$‎