On the uniform ergodic theorem

Michael Lin

doi:10.1090/S0002-9939-1974-0417821-6

On the uniform ergodic theorem

Michael Lin

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

108 Scopus citations

Abstract

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 language	English
Pages (from-to)	337-340
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	43
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1974-0417821-6
State	Published - 1 Jan 1974
Externally published	Yes

Keywords

Ergodic theorem
Markov operators
Quasi-compact operators

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1974-0417821-6

Cite this

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title = "On the uniform ergodic theorem",

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AB - 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.

KW - Ergodic theorem

KW - Markov operators

KW - Quasi-compact operators

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On the uniform ergodic theorem

Abstract

Keywords

ASJC Scopus subject areas

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