Abstract
In this paper certain subsequence ergodic theorems which have previously been known in the case of measure preserving point transformations are extended to Dunford-Schwartz operators, positive isometries, and power bounded Lamperti operators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Aaronson, M. Lin and B. Weiss,Mixing properties of Markov operators and ergodic transformations, and ergodicity of Cartesian products, Isr. J. Math.33 (1979), 198–224.
M. A. Akcoglu and A. del Junco,Convergence of averages of point transformations, Proc. Am. Math. Soc.49 (1975), 265–266.
M. A. Akcoglu and L. Sucheston,Dilations of positive contractions in L p spaces, Can. Math. Bull.20 (1977), 285–292.
J. R. Baxter and J. H. Olsen,Weighted and subsequential ergodic theorems, Can. J. Math.35 (1983), 145–166.
A. Bellow,Ergodic properties of isometries in L p spaces, 1<p< ∞, Bull. Am. Math. Soc.70 (1964), 366–371.
A. Bellow,Perturbation of a sequence, Advances in Mathematics, to appear.
A. Bellow, R. L. Jones and J. Rosenblatt,Convergence of moving averages, Ergodic Theory and Dynamical Systems10 (1990), 43–62.
A. Bellow and V. Losert,On sequences of density zero in ergodic theory, Contemporary Mathematics26 (1984), 49–60.
A. Bellow and V. Losert,The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences, Trans. Am. Math. Soc.288 (1985), 307–345.
J. Bourgain,On the maximal ergodic theorem for certain subsets of the integers, Isr. J. Math.61 (1988), 39–72.
J. Bourgain,On the pointwise ergodic theorem on L p for arithmetic sets, Isr. J. Math.61 (1988), 73–84.
J. Bourgain,Pointwise ergodic theorems for arithmetic sets, IHES Publication, October, 1989.
R. V. Chacon,A class of linear transformations, Proc. Am. Math. Soc.15 (1964), 560–564.
I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai,Ergodic Theory, Springer-Verlag, New York, 1982.
J. Doob,Stochastic Processes, Wiley, New York, 1953.
N. Dunford and J. Schwartz,Linear Operators, I, Wiley, New York, 1958.
S. R. Foguel,The Ergodic Theory of Markov Processes, Van Nostrand, New York, 1969.
P. R. Halmos,Lectures on Ergodic Theory, Math. Soc. Japan, 1956.
R. L. Jones,Inequalities for pairs of ergodic transformations, Radovi Matematicki4 (1988), 55–61.
R. L. Jones,Necessary and sufficient conditions for a maximal ergodic theorem along subsequences, Ergodic Theory and Dynamical Systems7 (1987), 203–210.
C. Kan,Ergodic properties of Lamperti operators, Can. J. Math.30 (1978), 1206–1214.
U. Krengel,Ergodic Theorems, De Gruyter Studies in Mathematics, 6, New York, 1985.
J. Lamperti,On the isometries of certain function spaces, Pacific J. Math.8 (1958), 459–466.
E. Lorch,Spectral Theory, Oxford University Press, New York, 1962.
J. Neveu,Mathematical Foundations of the Calculus of Probability, Holden-Day, San Francisco, 1965.
J. H. Olsen,Dominated estimates of convex combinations of commuting isometries, Isr. J. Math.11 (1972), 1–13.
V. A. Rohlin,On the fundamental ideas of measure theory, Mat. Sb.25, 107–150; Am. Math. Soc. Transl.71 (1952).
C. Ryll-Nardzewski,Topics in ergodic theory, inProceedings of the Winter School in Probability, Karpacz, Poland, Lecture Notes in Mathematics472, Springer-Verlag, Berlin, 1975, pp. 131–156.
M. Wierdl,Pointwise ergodic theorem along the prime numbers, Isr. J. Math.64 (1988), 315–336.
Author information
Authors and Affiliations
Additional information
Partially supported by NSF Grant DMS-8910947.
Rights and permissions
About this article
Cite this article
Jones, R.L., Olsen, J. Subsequence pointwise ergodic theorems for operators inL p . Israel J. Math. 77, 33–54 (1992). https://doi.org/10.1007/BF02808009
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02808009