On the Set of Topologically Invariant Means on an Algebra of Convolution Operators on L(g)


Let G be a locally compact group, Ap = Ap(G) the Banach algebra defined by Herz; thus A2(G) = A(G) is the Fourier algebra of G. Let PMp = Ap the dual, J ⊂ Ap a closed ideal, with zero set F = Z(J), and P = (Ap/J)∗. We consider the set TIMP(x) ⊂ P∗ of topologically invariant means on P at x ∈ F , where F is “thin.” We show that in certain cases card TIMP(x… (More)