Subsequence ergodic theorems for contractions
Authors:
Roger L. Jones, James Olsen and Máté Wierdl
Journal:
Trans. Amer. Math. Soc. 331 (1992), 837850
MSC:
Primary 47A35; Secondary 28D05, 47B38
MathSciNet review:
1043860
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Abstract: In this paper certain subsequence ergodic theorems which have previously been known in the case of measure preserving point transformations, or Dunford Schwartz operators, are extended to operators which are positive contractions on for fixed.
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 M. A. Akcoglu and L. Sucheston, Dilations of positive contractions in spaces, Canad. Math. Bull. 20 (1977), 285292. MR 0458230 (56:16433)
 [2]
 J. R. Baxter and J. H. Olsen, Weighted and subsequential ergodic theorems, Canad. J. Math. 35 (1983), 145166. MR 685822 (84g:47005)
 [3]
 A. Bellow and V. Losert, On sequences of density zero in ergodic theory, Contemp. Math., vol. 26, Amer. Math. Soc., Providence, R. I., 1984, pp. 4960. MR 737387 (86c:28034)
 [4]
 , The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences, Trans. Amer. Math. Soc. 288 (1985), 307345. MR 773063 (86c:28035)
 [5]
 J. Bourgain, On the maximal ergodic theorem for certain subsets of the integers, Israel J. Math. 61 (1988), 3972. MR 937581 (89f:28037a)
 [6]
 , An approach to pointwise ergodic theorems, GAFASeminar 1987, Lecture Notes in Math., vol. 1317, SpringerVerlag, Berlin, pp. 204223. MR 950982 (90b:28016)
 [7]
 , On the pointwise ergodic theorem on for arithmetic sets, Israel J. Math. 61 (1988), 7384. MR 937582 (89f:28037b)
 [8]
 , On the pointwise ergodic theorem for arithmetic sets, Inst. Hautes Études Sci. Publ. Math., Paris, 1989.
 [9]
 A. P. Calderón, Ergodic theory and translation invariant operators, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 349353. MR 0227354 (37:2939)
 [10]
 A. de la Torre, A simple proof of the maximal ergodic theorem, Canad. J. Math. 28 (1976), 10731075. MR 0417819 (54:5867)
 [11]
 R. L. Jones, Necessary and sufficient conditions for a maximal ergodic theorem along subsequences, Ergodic Theory Dynamical Systems 7 (1987), 203210. MR 896793 (88f:28013)
 [12]
 R. J. Jones and J. Olsen, Subsequence pointwise ergodic theorems for operators in , Israel J. Math. (to appear). MR 1194784 (94d:47008)
 [13]
 C. Kan, Ergodic properties of Lamperti operators, Canad. J. Math. 30 (1978), 12061214. MR 511557 (80g:47037)
 [14]
 J. Lamperti, On the isometries of certain function spaces, Pacific J. Math. 8 (1958). MR 0105017 (21:3764)
 [15]
 J. H. Olsen, Dominated estimates of convex combinations of commuting isometries, Israel J.Math. 11 (1972), 113. MR 0302862 (46:2005)
 [16]
 , The individual ergodic theorem for Lamperti contractions, C. R. Math. Rep. Acad. Sci. Canada 3 (1981), 113118. MR 612399 (82h:47008)
 [17]
 M. Wierdl, Pointwise ergodic theorem along the prime numbers, Israel J. Math. 64 (1988), 315336. MR 995574 (90f:11062)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199210438606
PII:
S 00029947(1992)10438606
Keywords:
Subsequences,
positive contractions,
Lamperti operators
Article copyright:
© Copyright 1992
American Mathematical Society
