  A linear map $u\colon \ E\to F$ 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.
