Weak Banach-Saks property in the space of compact operators

Document Type : Research Paper

Authors

1 Islamic Azad University, Bafgh Branch

2 Yazd University

Abstract

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 $psi_{y^*}(T)= T^*y^*.$‎

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  • Receive Date: 12 October 2012
  • Revise Date: 05 March 2013
  • Accept Date: 08 April 2013
  • First Publish Date: 01 April 2014