The behavior of iterates of multipliers in commutative Banach algebras
Volume 128 / 2022
Annales Polonici Mathematici 128 (2022), 233-247
MSC: Primary 46Hxx, 43A10; Secondary 43A20, 43A22.
DOI: 10.4064/ap210627-2-12
Published online: 9 March 2022
Abstract
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\in A) $. Some related problems are also discussed.
