Let A be a complex commutative semisimple Banach algebra. In this paper, we study some ergodic properties of Cesaro bounded multipliers on A. The results are linked to the sets of synthesis and the main applications are concerned with Fourier and Fourier-Stieltjes algebras on locally compact groups. We study also the structure of ideals associated with multipliers of A and A-invariant projections of the dual space of A. Some related problems are also discussed.