Convolutions on compact groups and Fourier algebras of coset spaces
We study two related questions. (1) For a compact group G, what are the ranges of the convolution maps on A(G × G) given for u,v in A(G) by u × v ↦ u*v̌ (v̌(s) = v(s^-1)) and u × v ↦ u*v? (2) For a locally compact group G and a compact subgroup K, what are the amenability properties of the Fourier algebra of the coset space A(G/K)? The algebra A(G/K) was defined and studied by the first named author. In answering the first question, we obtain, for compact groups which do not...