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Two Consequences of Brunel's Theorem

Published online by Cambridge University Press:  20 November 2018

James H. Olsen
James H. Olsen*
Affiliation:
Department of Mathematics, North Dakota State University, 300 Mindard Hall, SU Station, P. O. Box 5075, Fargo, ND, 58105-5075, USA
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Abstract

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In this note we observe two consequences of Brunei's recent theorem. If T1,..., Tn are majorized by positive power-bounded operators S1,..., Sn of Lp, 1 < p < ∞, for which the ergodic theorem holds, then a multiple sequence ergodic theorem holds for T1,....,Tn. Further, the individual convergence for each Tk can be taken along uniform sequences.

Keywords

47A3528D99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 105 - 108
Copyright
Copyright © Canadian Mathematical Society 1991

References

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