Some Mean and Uniform Ergodic Type Theorems

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Oğuz G., ORHAN C.

Filomat, vol.36, no.7, pp.2403-2410, 2022 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 36 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2207403o
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.2403-2410
  • Keywords: bounded linear operator, Cesàro average, ergodic decomposition, Ergodic theorem, mean ergodic theorem, power bounded operator, regular matrix, uniform ergodic theorem
  • Open Archive Collection: AVESIS Open Access Collection
  • Ankara University Affiliated: Yes

Abstract

© 2022, University of Nis. All rights reserved.Let X be a Banach space and T ∈ B(X). Cohen determined a class of regular infinite matrices ∑ A = (ank) for which (formula presented) converges strongly to an element invariant under T. In the present paper k=1 we study A-mean and A-uniform ergodic type results when A = (ank) is a regular infinite matrix satisfying Cohen’s uniformity condition lim (formula presented) uniformly in n.