The centre of the bidual of Fourier algebras (discrete groups)

Abstract

For a discrete group G with Fourier algebra A(G), we study the topological centre $Z_t$ of the bidual. If G is amenable, then $Z_t$ = A(G). But if G contains a non-abelian free group $F_r$, we show that $Z_t$ is strictly larger than A(G). Furthermore, it is shown that the subalgebra of radial functions in A(G) is Arens regular.