On the uniform ergodic theorem. II

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33 Scopus citations


Let (Tt) be a strongly continuous semigroup of bounded linear operators on a Banach space X, satisfying equation omited. We prove the equivalence of the following conditions: (1) t-1 equation omited converges uniformly as t → ∞. (2) The infinitesimal generator A has closed range. (3) Equation omitedexists in the uniform operator topology.

Original languageEnglish
Pages (from-to)217-225
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - 1 Jan 1974
Externally publishedYes


  • Abelergodicity
  • Ergodic theorem
  • Ergodicity of semigroups

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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