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Quasi-compactness and uniform ergodicity of positive operators

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Abstract

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

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Authors and Affiliations

  1. Ben Gurion University of the Negev, Beer Sheva, Israel

    Michael Lin

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  1. Michael Lin
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Lin, M. Quasi-compactness and uniform ergodicity of positive operators. Israel J. Math. 29, 309–311 (1978). https://doi.org/10.1007/BF02762018

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  • DOI: https://doi.org/10.1007/BF02762018

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