On the uniform ergodic theorem in invariant subspaces.

  • Abdelaziz Tajmouati Sidi Mohamed Ben Abdellah University. https://orcid.org/0000-0003-1572-1241
  • Abdeslam El Bakkali Chouaib Doukkali University.
  • Fatih Barki Sidi Mohamed Ben Abdellah University.
Keywords: Uniform ergodic theorem, Cesàro averages, Decomposition ergodic


Let T be a bounded linear operator on a Banach space X into itself. In this paper, we study the uniform ergodicity of the operator T|Y when Y is a closed subspace invariant under T. We show that if T satisfies, lim n → ∞ ‖ T n ‖ n = 0 , then T is uniformly ergodic on X if and only if the restriction of T to some closed subspace Y ⊂ X, invariant under T and R[(I − T)k] ⊂ Y for some integer k ≥ 1, is uniformly ergodic. Consequently, we obtain other equivalent conditions concerning the theorem of Mbekhta and Zemànek [9], theorem 1), also to the theorem of the Gelfand-Hille type.  

Author Biographies

Abdelaziz Tajmouati, Sidi Mohamed Ben Abdellah University.
Faculty of Sciences Dhar El Mahraz.
Abdeslam El Bakkali, Chouaib Doukkali University.
Faculty of Sciences.
Fatih Barki, Sidi Mohamed Ben Abdellah University.
Faculty of Sciences Dhar El Mahraz.


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How to Cite
A. Tajmouati, A. El Bakkali, and F. Barki, “On the uniform ergodic theorem in invariant subspaces.”, Proyecciones (Antofagasta, On line), vol. 38, no. 2, pp. 315-324, May 2019.