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This work deals with various questions concerning Fourier multipliers on $L^p$, Schur multipliers on the Schatten class $S^p$ as well as their completely bounded versions when $L^p$ and $S^p$ are viewed as operator spaces. For this purpose we use subsets of ℤ enjoying the non-commutative Λ(p)-property which is a new analytic property much stronger than the classical Λ(p)-property. We start by studying the notion of non-commutative Λ(p)-sets in the general case of an arbitrary discrete group before turning to the...