Completely co-bounded Schur multipliers

Abstract

A linear map $u:E\to F$ between operator spaces is called completely co-bounded if it is completely bounded as a map from $E$ to the opposite of $F$. We give several simple results about completely co-bounded Schur multipliers on $B({\ell }_2)$ and the Schatten class $S_p$. We also consider Herz-Schur multipliers on groups.