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July 2018 Pointwise entangled ergodic theorems for Dunford–Schwartz operators
Dávid Kunszenti-Kovács
Banach J. Math. Anal. 12(3): 634-650 (July 2018). DOI: 10.1215/17358787-2017-0062

Abstract

We investigate pointwise convergence of entangled ergodic averages of Dunford–Schwartz operators T0,T1,,Tm on a Borel probability space. These averages take the form

1Nk1n1,,nkNTmnα(m)Am1Tm1nα(m1)A2T2nα(2)A1T1nα(1)f, where fLp(X,μ) for some 1p<, and α:{1,,m}{1,,k} encodes the entanglement. We prove that, under some joint boundedness and twisted compactness conditions on the pairs (Ai,Ti), convergence holds almost everywhere for all fLp. We also present an extension to polynomial powers in the case p=2, in addition to a continuous version concerning Dunford–Schwartz C0-semigroups.

Citation

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Dávid Kunszenti-Kovács. "Pointwise entangled ergodic theorems for Dunford–Schwartz operators." Banach J. Math. Anal. 12 (3) 634 - 650, July 2018. https://doi.org/10.1215/17358787-2017-0062

Information

Received: 12 September 2017; Accepted: 3 December 2017; Published: July 2018
First available in Project Euclid: 19 April 2018

zbMATH: 06946074
MathSciNet: MR3824744
Digital Object Identifier: 10.1215/17358787-2017-0062

Subjects:
Primary: 47A35
Secondary: 37A30, 47B38

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.12 • No. 3 • July 2018
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