Oğuz, GencayOrhan, Cihan2021-11-092021-11-092019-08-01https://doi.org/10.31801/cfsuasmas.562214http://hdl.handle.net/20.500.12575/75960Let T be a bounded linear operator on a Banach space X . Replacing the Ces\`{a}ro matrix by a regular matrix A = ( a n j ) Cohen studied a mean ergodic theorem. In the present paper we extend his result by taking a sequence of infinite matrices A = ( A ( i ) ) that contains both convergence and almost convergence. This result also yields an A -ergodic decomposition. When T is power bounded we give a characterization for T to be A -ergodic.enInfinite matricesAlmost convergenceErgodic theoremsArticle682226422712618-6470