ANNALES POLONICI MATHEMATICI, vol.128, pp.233-247, 2022 (SCI-Expanded)
Let A be a complex, commutative, and semisimple Banach algebra and let T be a power bounded multiplier on A. We prove a Katznelson-Tzafriri type theorem for T. As an application, we give some results concerning convergence of the sequence {T(n)a} (a is an element of A). Some related problems are also discussed.