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This work deals with various questions concerning Fourier multipliers on L, Schur multipliers on the Schatten class S as well as their completely bounded versions when L and S are viewed as operator spaces. We use for this aim 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 group Z. AMS classification (1991): primary 43A22, 43A46, 46L50, secondary 46B70, 47B10, 47D15.

Fourier analysis, Schur multipliers on $S^p$ and non-commutative Λ(p)-sets