Distance Formulas in Group Algebras

Abstract

Let G be a locally compact amenable group, A (G) and B (G) be the Fourier and the Fourier-Stieltjes algebra of G, respectively. For a given u is an element of B (G), let epsilon(u):={g is an element of G : vertical bar u(g)vertical bar = 1}. The main result of this paper particularly states that if parallel to u parallel to(B(G)) <= 1 and <(u(epsilon(u)))over bar>is countable (in particular, if epsilon(u) is compact and scattered), then lim(n ->infinity) parallel to u(n)v parallel to(A(G)) = dist (v, I-epsilon u ),for all v is an element of A (G), where I-epsilon u = {v is an element of A (G) : v(g = 0, for all g is an element of epsilon(u) )}. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.