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

Abstract 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 ∈ N ‖ u n ‖ ∞ . 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 ∈ N , v ∈ B ( G ) .