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.
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Review Articles |
Authors | |
Publication Date | August 1, 2019 |
Submission Date | May 9, 2019 |
Acceptance Date | June 17, 2019 |
Published in Issue | Year 2019 Volume: 68 Issue: 2 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
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