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The Individual Ergodic Theorem for Contractions with Fixed Points

Published online by Cambridge University Press:  20 November 2018

James H. Olsen
James H. Olsen*
Affiliation:
Department of Mathematical Sciences, North Dakota State University, Fargo, North Dakota 58105
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Let (X, I, μ) be a σ-finite measure space and let T take Lp to Lp, p fixed, 1<p<∞,‖t‖p≤1. We shall say that the individual ergodic theorem holds for T if for any uniform sequence K1, k2,… (for the definition, see [2]) and for any f∊LP(X), the limit

exists and is finite almost everywhere.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 1 , 01 March 1980 , pp. 115 - 116
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Akcoglu, M. A., A Pointwise Ergodic Theorem in Lp-Spaces, Can. J. Math. 27 (1975), 1075-1082.Google Scholar
2. Brunei, A. and Keane, M., Ergodic Theorems for Operator Sequences, Z. Wahrscheinlichkeitstheorie Veru. Geb. 12 (1969), pp. 231-240.Google Scholar
3. De La Torre, A., A dominated Ergodic Theorem for Contractions with Fixed Points, Canad. Math. Bull., 20 (1977), 89-91.Google Scholar
4. Sato, R., On the Individual Ergodic Theorem for Subsequences, Studia Mathematica, T. 45 (1973), 31-35.Google Scholar