Fourier-Stieltjes transforms and weakly almost periodic functionals for compact groups

Abstract

Let G be a compact group and H a closed subgroup. A function in the Fourier algebra of H can be extended to a function in the Fourier algebra of G without increase in norm and with an arbitrarily small increase in sup-norm. For G a compact Lie group, the space of Fourier-Stieltjes transforms is not dense in the space of weakly almost periodic functionals on the Fourier algebra of (?.