MEAN ERGODIC TYPE THEOREMS

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Oguz G., Orhan C.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.68, no.2, pp.2264-2271, 2019 (ESCI)

• Publication Type: Article / Article
• Volume: 68 Issue: 2
• Publication Date: 2019
• Doi Number: 10.31801/cfsuasmas.562214
• Journal Name: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
• Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Page Numbers: pp.2264-2271
• Keywords: Infinite matrices, almost convergence, ergodic theorems, SUMMABILITY
• Ankara University Affiliated: Yes

Abstract

Let T be a bounded linear operator on a Banach space X. Replacing the Cesaro 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 A = (A((i))) that contains both convergence and almost convergence. This result also yields an A-ergodic decomposition. When T is power bounded we give a characterization for T to be A-ergodic.