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 supn∈N‖un‖<∞. 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 (vn)n∈N, v∈B(G).