Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401Weak Banach-Saks property in the space of compact operators521530513ENB. KhadijehMoosaviIslamic Azad University, Bafgh BranchS. MohammadMoshtaghiounYazd UniversityJournal Article20121012For 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 $psi_{y^*}(T)= T^*y^*.$http://bims.iranjournals.ir/article_513_d1178361f94ff0d658d4159f2e3bc59b.pdf