Schur Multipliers with Unequal Operator and Completely Bounded Norms on $S_p$, $1<p\ne 2<\infty $

For every $1<p\neq2<\infty$, we exhibit an explicit Schur multiplier on $S_p$ whose operator norm is strictly smaller than its completely bounded norm. More precisely, for each such $p$, we construct a finitely supported Schur symbol $m_p$ such that \[ \|M_{m_p}\|_{p\to p} < \|M_{m_p}\|_{\math