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Akcoglu's Ergodic Theorem for Uniform Sequences

Published online by Cambridge University Press:  20 November 2018

James H. Olsen
James H. Olsen*
Affiliation:
North Dakota State University, Fargo, North Dakota
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Let (X, F,) be a sigma-finite measure space. In what follows we assume p fixed, 1 < p < ∞ . Let T be a contraction of Lp(X, F, μ) (‖T‖,p ≦ 1). If ƒ ≧ 0 implies Tƒ ≧ 0 we will say that T is positive. In this paper we prove that if is a uniform sequence (see Section 2 for definition) and T is a positive contraction of Lp, then

exists and is finite almost everywhere for every ƒ ∊ Lp(X, F, μ).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 4 , April 1980 , pp. 880 - 884
Copyright
Copyright © Canadian Mathematical Society 1980

References

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3. Lorch, R. L., Spectral theory (Oxford, 1962).Google Scholar
4. Sato, R., On the individual ergodic theorem for subsequences, Studia Mathematica. TXL. V. (1973), 31–35.Google Scholar