Mustafayev, Heybetkulu2025-05-102025-05-1020200025-55211903-180710.7146/math.scand.a-1196012-s2.0-85107511685https://doi.org/10.7146/math.scand.a-119601https://hdl.handle.net/20.500.14720/14003Let G be a locally compact abelian group and let M(G) be the measure algebra of G. A measure mu is an element of M(G) is said to be power bounded if sup(n >= 0) parallel to mu(n)parallel to(1) < infinity. Let T = {T-g : g is an element of G} be a bounded and continuous representation of G on a Banach space X. For any mu is an element of M(G), there is a bounded linear operator on X associated with mu, denoted by T-mu, which integrates T-g with respect to mu. In this paper, we study norm and almost everywhere behavior of the sequences {T-mu(n) x} (x is an element of X) in the case when mu, is power bounded. Some related problems are also discussed.eninfo:eu-repo/semantics/closedAccessArticle1262Q4Q4339366WOS:000546562500014