Ordered invariant ideals of fourier-stieltjes algebras

For a locally compact group G, every G-invariant subspace E of the Fourier-Stieltjes algebra B(G) gives rise to the following two ideals of the group C^∗-algebra C^∗(G): the intersection of the kernels of the representations with many coefficient functions in E, and the preannihilator of E. We investigate the question of whether these two ideals coincide. This leads us to define and study two properties of E — ordered and weakly ordered — that measure how many positive definite functions E contains.