On the uniform ergodic theorem. II

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

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
Volume46
Issue number2
DOIs
StatePublished - 1 Jan 1974
Externally publishedYes

Keywords

  • Abelergodicity
  • Ergodic theorem
  • Ergodicity of semigroups

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'On the uniform ergodic theorem. II'. Together they form a unique fingerprint.

Cite this