Measurable Schur multipliers and completely bounded multipliers of the Fourier algebra

Let G be a locally compact group L^p(G) be the usual L^p-space for 1 =< p =< infty 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 M_{cb}A(G). We show that M_{cb}A(G) can be characterised as the ``invariant part'' of the space of (completely...More