On the set of topologically invariant means on an algebra of convolution operators on L(p)(G)

Let G be a locally compact group, A(p) = A(p)(G) the Banach algebra defined by Herz; thus A(2)(G) = A(G) is the Fourier algebra of G. Let PM(p) = A(p)* the dual, J subset of A(p) a closed ideal, with zero set F = Z(J), and P = (A(p)/J)*. We consider the set TIM(p)(x) subset of P* of topologically invariant means on P at x is an element of F, where F is ''thin''. We show that in certain cases card TIM(p)(x) greater than or equal to 2(c) and TIM(p)(x) does not have the WRNP, i.e. is far from being weakly compact in P*. This implies the non-Arens regularity of the algebra A(p)/J.