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.
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 1 Ağustos 2019 |
Gönderilme Tarihi | 9 Mayıs 2019 |
Kabul Tarihi | 17 Haziran 2019 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 68 Sayı: 2 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
This work is licensed under a Creative Commons Attribution 4.0 International License.