Weak-closedness of subspaces of fourier-stieltjes algebras and weak-continuity of the restriction map

Let G be a locally compact group and B(G) the Fourier-Stieltjes algebra of G. We study the problem of how weak-closedness of some translation invariant subspaces of B(G) is related to the structure of G. Moreover, we prove that for a closed subgroup H of G, the restriction map from B(G) to B(H) is weak-continuous only when H is open in G.