Quasi-compactness and uniform ergodicity of positive operators

Michael Lin

doi:10.1007/BF02762018

Quasi-compactness and uniform ergodicity of positive operators

Michael Lin

Department of Mathematics

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

19 Scopus citations

Abstract

The following converse to the Yosida-Kakutani theorem is proved: If T is a positive operator on a Banach lattice with {norm of matrix}Tⁿ{norm of matrix}/n → 0, then T is quasi-compact if (and only if) the averages of its iterates converge uniformly to a finite-dimensional projection.

Original language	English
Pages (from-to)	309-311
Number of pages	3
Journal	Israel Journal of Mathematics
Volume	29
Issue number	2-3
DOIs	https://doi.org/10.1007/BF02762018
State	Published - 1 Jun 1978

ASJC Scopus subject areas

General Mathematics

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10.1007/BF02762018

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abstract = "The following converse to the Yosida-Kakutani theorem is proved: If T is a positive operator on a Banach lattice with {norm of matrix}T n{norm of matrix}/n → 0, then T is quasi-compact if (and only if) the averages of its iterates converge uniformly to a finite-dimensional projection.",

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AB - The following converse to the Yosida-Kakutani theorem is proved: If T is a positive operator on a Banach lattice with {norm of matrix}T n{norm of matrix}/n → 0, then T is quasi-compact if (and only if) the averages of its iterates converge uniformly to a finite-dimensional projection.

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Quasi-compactness and uniform ergodicity of positive operators

Abstract

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