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Pointwise ergodic theorems for bounded Lamperti representations of amenable groups


Author: A. Tempelman
Journal: Proc. Amer. Math. Soc. 143 (2015), 4989-5004
MSC (2010): Primary 22D40; Secondary 37A30
DOI: https://doi.org/10.1090/proc/12616
Published electronically: April 3, 2015
MathSciNet review: 3391055
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Abstract: Dominated and Pointwise Ergodic Theorems for bounded representations of second countable locally compact amenable groups by Lamperti operators in $ L^p(\Omega ,\mathcal F, m),$ $ p>1$ fixed, are proved; we restrict ourselves to Cesàro averages in this paper. These theorems generalize or are closely related to well-known theorems for powers of power bounded Lamperti operators.


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Additional Information

A. Tempelman
Affiliation: Department of Mathematics and Department of Statistics, The Pennsylvania State University, 325 Thomas Building, University Park, Pennsylvania 16802

DOI: https://doi.org/10.1090/proc/12616
Received by editor(s): January 26, 2014
Received by editor(s) in revised form: January 30, 2014, February 3, 2014, and August 20, 2014
Published electronically: April 3, 2015
Communicated by: Nimish Shah
Article copyright: © Copyright 2015 American Mathematical Society

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