Open Access
April 2017 Ergodic behaviors of the regular operator means
Laurian Suciu
Banach J. Math. Anal. 11(2): 239-265 (April 2017). DOI: 10.1215/17358787-3796878


This article deals with some ergodic properties for general sequences in the closed convex hull of the orbit of some (not necessarily power-bounded) operators in Banach spaces. A regularity condition more general than that of ergodicity is used to obtain some versions of the Esterle–Katznelson–Tzafriri theorem. Also, the ergodicity of the backward iterates of a sequence is proved under appropriate assumptions as, for example, its peripheral boundedness on the unit circle. The applications concern uniformly Kreiss-bounded operators, and other ergodic results are obtained for the binomial means and some operator means related to the Cesàro means.


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Laurian Suciu. "Ergodic behaviors of the regular operator means." Banach J. Math. Anal. 11 (2) 239 - 265, April 2017.


Received: 19 January 2016; Accepted: 1 April 2016; Published: April 2017
First available in Project Euclid: 14 January 2017

zbMATH: 06694352
MathSciNet: MR3597562
Digital Object Identifier: 10.1215/17358787-3796878

Primary: 47A35
Secondary: 47A10 , 47A16

Keywords: binomial mean , Cesàro mean , ergodicity , uniform Kreiss-bounded operator

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 2 • April 2017
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