MEAN ERGODIC TYPE THEOREMS

Abstract

Let T be a bounded linear operator on a Banach space X. Replacing the Ces‡ro matrix by a regular matrix A = (anj ) Cohen studied amean ergodic theorem. In the present paper we extend his result by taking asequence of inÖnite matrices A = (A(i)) that contains both convergence andalmost convergence. This result also yields an A-ergodic decomposition. WhenT is power bounded we give a characterization for T to be A-ergodic.