Weak Banach-Saks property in the space of compact operators

Document Type : Research Paper


1 Islamic Azad University, Bafgh Branch

2 Yazd University


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 operators on $mathcal{M}$ are defined by‎ ‎$phi_x(T)= Tx$ and $psi_{y^*}(T)= T^*y^*.$‎


Main Subjects