- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 68 Issue: 2
- Mean ergodic type theorems
Mean ergodic type theorems
Authors : Gencay Oğuz, Cihan Orhan
Pages : 2264-2271
Doi:10.31801/cfsuasmas.562214
View : 6 | Download : 4
Publication Date : 2019-08-01
Article Type : Research
Abstract :Let $T$ be a bounded linear operator on a Banach space $X$. Replacing the Ces\`{a}ro matrix by a regular matrix $A=(a_{nj})$ Cohen studied a mean ergodic theorem. In the present paper we extend his result by taking a sequence of infinite matrices $\mathcal{A}=(A^{(i)})$ 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