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On power-subadditive positive operators on the $ L_p$ spaces $ (1<p<\infty)$


Author: Jean-Claude Lootgieter
Journal: Proc. Amer. Math. Soc. 145 (2017), 4299-4311
MSC (2010): Primary 47A35
DOI: https://doi.org/10.1090/proc/13124
Published electronically: June 16, 2017
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Abstract: In this article, we first give a counterexample to the statement appearing in a note of A. Brunel in 2002 concerning the study of positive operators on $ L_p$ spaces $ (1<p<\infty )$ whose sequence of powers is subadditive. We then give some properties of these operators when they are power-bounded.


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Additional Information

Jean-Claude Lootgieter
Affiliation: Université Pierre et Marie Curie, 3 place de l’Escadrille Normandie Niemen 75013, Paris, France
Email: jean-claude.lootgieter@upmc.fr

DOI: https://doi.org/10.1090/proc/13124
Keywords: Positive linear operator with subadditive powers, dominated ergodic estimate, pointwise ergodic theorem
Received by editor(s): December 2, 2013
Received by editor(s) in revised form: July 8, 2015, October 23, 2015, January 7, 2016, and January 21, 2016
Published electronically: June 16, 2017
Communicated by: Nimish A. Shaw
Article copyright: © Copyright 2017 American Mathematical Society

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