Mustafayev, Heybetkulu2025-05-102025-05-1020170004-97271755-163310.1017/S00049727170003512-s2.0-85021742563https://doi.org/10.1017/S0004972717000351https://hdl.handle.net/20.500.14720/5764Let G be a locally compact amenable group and A(G) and B(G) be the Fourier and the Fourier-Stieltjes algebras of G; respectively. For a power bounded element u of B(G), let epsilon(u) : = {g is an element of G : |u(g)| = 1}. We prove some convergence theorems for iterates of multipliers in Fourier algebras. (a) If parallel to u parallel to(B(G)) <= 1, then lim(n ->infinity) parallel to u(n)v parallel to(A(G)) = dist(v, I epsilon(u)) for v is an element of A(G), where I-epsilon u = {v is an element of A(G) : v(epsilon(u)) = {0}}. (b) The sequence {u(n)v}(n is an element of N) converges for every v is an element of A(G) if and only if epsilon(u) is clopen and u(epsilon(u)) = {1}. (c) If the sequence {u(n)v}(n is an element of N) converges weakly in A(G) for some v is an element of A(G), then it converges strongly.eninfo:eu-repo/semantics/closedAccessLocally Compact GroupFourier AlgebraFourier-Stieltjes AlgebraConvergenceArticle963Q3Q3487495WOS:000414442000016