Spectral synthesis for A(G) and subspaces of VN(G)

Let G be a locally compact group, A(G) the Fourier algebra of G and VN(G) t he von Neumann algebra generated by the left regular representation of G. W e introduce the notion of X-spectral set and X-Ditkin set when X is an A(G) -invariant linear subspace of VN(G), thus providing a unified approach to b oth spectral and Ditkin sets and their local variants. Among other things, we prove results on unions of X-spectral sets and X-Ditkin sets, and an inj ection theorem for X-spectral sets.