On the uniform ergodic theorem. II

Michael Lin

doi:10.1090/S0002-9939-1974-0417822-8

On the uniform ergodic theorem. II

Michael Lin

Research output: Contribution to journal › Article › peer-review

36 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 language	English
Pages (from-to)	217-225
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	46
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1974-0417822-8
State	Published - 1 Jan 1974
Externally published	Yes

Keywords

Abelergodicity
Ergodic theorem
Ergodicity of semigroups

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1974-0417822-8

Cite this

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AB - 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.

KW - Abelergodicity

KW - Ergodic theorem

KW - Ergodicity of semigroups

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On the uniform ergodic theorem. II

Abstract

Keywords

ASJC Scopus subject areas

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