Mean ergodic type theorems

Year 2019, Volume: 68 Issue: 2, 2264 - 2271, 01.08.2019

Gencay Oğuz Cihan Orhan

https://doi.org/10.31801/cfsuasmas.562214

Cited By: 1

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

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