Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-20T11:29:46.175Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Baxter, J. R. and Olsen, J. H., Weighted and subsequential ergodic theorems, Can. J. Math. 35, 145–166.Google Scholar
2. Bellow, A. and Losert, V., The weighted pointwise ergodic theorem along subsequences, TAMS 288, 307– 346.Google Scholar
3. Brunei, A., A pointwise ergodic theorem for positive, Cesaro bounded operators on Lp(1 < p < ∞), proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Columbus, Ohio, June 11-14, 1988, ed. by Edgar, G. A. and Sucheston, L., Academic Press, 1989, 153–157.Google Scholar
4. Brunei, A. and Keane, M., Ergodic theorems for operator sequences, ZW 12, 231–240.Google Scholar
5. McGrath, S. A., Some ergodic theorems for commuting L1 contractions, Studia Math. 70, 165–172.Google Scholar
6. Frangos, N. E. and Louis Sucheston, On multiparameter ergodic and martingale theorems in infinite measure spaces, Probab. Th. Rel. Fields 71 (1986), 477–490.Google Scholar
7. Olsen, J. H., Akcoglu's ergodic theorem for uniform sequences, Can. J. Math. 32, 880–884.Google Scholar
8. Olsen, J. H., A multiple sequence ergodic theorem, Can. Math. Bull. 26, 493—497.Google Scholar
9. Olsen, J. H., Multi-parameter weighted ergodic theorems from their single parameter version, Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Columbus, Ohio, June 11-14, 1988, ed. by Edgar, G. A. and Sucheston, L., Academic Press, 1989, 297–303.Google Scholar