On the uniform ergodic theorem

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104 Scopus citations


We give an elementary proof of the uniform ergodic theorem: "Let T be a linear operator on a Banach space with r"/n-K). The following are equivalent: (1) N-1 2'n=J T" converges uniformly. (2) (1-Tf-Xis closed. (3) (I-T)Xis closed.

Original languageEnglish
Pages (from-to)337-340
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - 1 Jan 1974
Externally publishedYes


  • Ergodic theorem
  • Markov operators
  • Quasi-compact operators

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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