The structure of power bounded elements in Fourier-Stieltjes algebras of locally compact groups

Let G be an arbitrary locally compact group and B(G) its Fourier-Stieltjes algebra. An element u of B(G) is called power bounded if sup(n is an element of N) parallel to u(n)parallel to < infinity. We present a detailed analysis of the structure of power bounded elements of B(G) and characterize them in terms of sets in the coset ring of G and w*-convergence of sequences (v(n))(n is an element of N), v is an element of B(G). (C) 2012 Elsevier Masson SAS. All rights reserved.