  This paper is concerned with weak* closed masa-bimodules generated by
A(G)-invariant subspaces of VN(G). An annihilator formula is established, which
is used to characterise the weak* closed subspaces of B(L^2(G)) which are
invariant under both Schur multipliers and a canonical action of M(G) on
B(L^2(G)) via completely bounded maps. We study the special cases of extremal
ideals with a given null set and, for a large class of groups, we establish a
link between relative spectral synthesis and relative operator synthesis.
