Mean ergodic type theorems

Authors : Gencay OĞUZ, Cihan ORHAN

Pages : 2264-2271

Doi:10.31801/cfsuasmas.562214

View : 18 | Download : 13

Publication Date : 2019-08-01

Article Type : Research Paper

Abstract :Let $T$ be a bounded linear operator on a Banach space $X$. Replacing the Ces\`{a}ro matrix by a regular matrix $A=insert ignore into journalissuearticles values(a_{nj});$ Cohen studied a mean ergodic theorem. In the present paper we extend his result by taking a sequence of infinite matrices $\mathcal{A}=insert ignore into journalissuearticles values(A^{insert ignore into journalissuearticles values(i);});$ that contains both convergence and almost convergence. This result also yields an $\mathcal{A}$-ergodic decomposition. When $T$ is power bounded we give a characterization for $T$ to be $\mathcal{A}$-ergodic.
Keywords : Infinite matrices, almost convergence, ergodic theorems