Pisier's conjecture on bounded and completely bounded Schur multipliers

Let $d4d8_p$ be the collection of symbols that are bounded Schur multipliers of the Schatten–von Neumann class $d4d4_p$, and let $d4d8_p^{\mathrm{cb}}$ be the collection of symbols that are completely bounded Schur multipliers of $d4d4_p$. For $1<p\ne2<\infty$, Pisier's conjecture.

$$\mathcal{M}_p\ne\mathcal{M}_p^{\mathrm{cb}}.$$

The conjecture concerns whether boundedness and complete boundedness differ for Schur multipliers on Schatten classes; the source presents it as an open question attributed to Pisier.