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A Multiple Sequence Ergodic Theorem

Published online by Cambridge University Press:  20 November 2018

James H. Olsen
James H. Olsen*
Affiliation:
North Dakota State University
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Abstract

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Let be a σ-finite measure space, {T1, …, Tk} a set of linear operators of , some p, 1≤p≤∞.If

exists a.e. for all f ∊ Lp, we say that the multiple sequence ergodic theorem holds for {T1, …, Tk}. If f≥0 implies Tf≥0, we say that T is positive. If there exists an operator S such that |Tf(x)|≥S |f|(x) a.e., we say that T is dominated by S. In this paper we prove that if T1, …, Tk are dominated by positive contractions of , p fixed, 1<p<∞, then the multiple sequence ergodic theorem holds for {T1, …, Tk}.

Keywords

47A3528A65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 4 , 01 December 1983 , pp. 493 - 497
Copyright
Copyright © Canadian Mathematical Society 1983

References

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