# Measurable Schur Multipliers and Completely Bounded Multipliers of the Fourier Algebras

@article{Spronk2002MeasurableSM, title={Measurable Schur Multipliers and Completely Bounded Multipliers of the Fourier Algebras}, author={Nico Spronk}, journal={Proceedings of the London Mathematical Society}, year={2002}, volume={89} }

Let G be a locally compact group, Lp(G) be the usual Lp‐space for 1 ⩽ p ⩽ ∞, and A(G) be the Fourier algebra of G. Our goal is to study, in a new abstract context, the completely bounded multipliers of A(G), which we denote McbA(G). We show that McbA(G) can be characterised as the ‘invariant part’ of the space of (completely) bounded normal L∞(G)‐bimodule maps on B(L2(G)), the space of bounded operators on L2(G). In doing this we develop a function‐theoretic description of the normal L∞(X…

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