On the Limited p-Schur Property of Some Operator Spaces

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M.B. Dehghani, S.M. Moshtaghioun, M. Dehghani, On the Limited p-Schur Property of Some Operator Spaces, Int. J. Anal. Appl., 16 (1) (2018), 50-61.

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M.B. Dehghani, S.M. Moshtaghioun, M. Dehghani

Abstract

We introduce and study the notion of limited $p$-Schur property ($1\leq p\leq\infty$) of Banach spaces. Also, we establish some necessary and sufficient conditions under which some operator spaces have the limited $p$-Schur property. In particular, we prove that if $X$ and $Y$ are two Banach spaces such that $X$ contains no copy of $\ell_1$ and $Y$ has the limited $p$-Schur property, then $K(X,Y)$ (the space of all compact operators from $X$ into $Y$) has the limited $p$-Schur property.

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