A separation property of positive definite functions on locally compact groups and applications to Fourier algebras

For a closed subgroup H of a locally compact group G consider the property that the continuous positive definite functions on G which are identically one on H separate points in G/H from points in H. We prove a structure theo rem for almost connected groups having this separation property for every c losed subgroup. Also, when a pair (G, H) has this separation property, ther e are interesting consequences in the ideal theory of the Fourier algebra o f G. (C) 2000 Academic Press.