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A Pointwise Ergodic Theorem in Lp-Spaces

Published online by Cambridge University Press:  20 November 2018

M. A. Akcoglu
M. A. Akcoglu*
Affiliation:
University of Toronto, Toronto, Ontario
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Let be a measure space and the usual Banach spaces. A linear operator T : Lp → Lpis called a positive contraction if it transforms non-negative functions into non-negative functions and if its norm is not more than one. The purpose of this note is to show that if 1 < p < ∞ and if T : Lp → Lp is a positive contraction then

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1075 - 1082
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Akcoglu, M. A. and Sucheston, L., On the dominated ergodic theorem in L-2 space (to appear in Froc. Amer. Math. Soc).Google Scholar
2. Burkholder, D. L., Semi-Gaussian subspaces, Trans. Amer. Math. Soc. 104 (1902), 123–131.Google Scholar
3. Chacon, R. V. and Olsen, J., Dominated estimates of positive contractions, Proc. Amer. Math. Soc. 20 (1969), 266–271.Google Scholar
4. Chacon, R. V. and McGrath, S. A., Estimates of positive contractions, Pacific J. Math. 30 (1969), 609–620.Google Scholar
5. Ionescu-Tulcea, A., Ergodic properties of isometries in Lp-spaces, Bull. Amer. Math. Soc. 70 (1964), 366–371.Google Scholar
6. Stein, E. M., On the maximal ergodic theorem, Proc. Nat. Acad. Sci. U.S.A. J,7 (1961), 1894–1897.Google Scholar