Subsequence ergodic theorems for contractions

Authors:
Roger L. Jones, James Olsen and Máté Wierdl

Journal:
Trans. Amer. Math. Soc. **331** (1992), 837-850

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.

**[1]**M. A. Akcoglu and L. Sucheston,*Dilations of positive contractions on 𝐿_{𝑝} spaces*, Canad. Math. Bull.**20**(1977), no. 3, 285–292. MR**0458230****[2]**J. R. Baxter and J. H. Olsen,*Weighted and subsequential ergodic theorems*, Canad. J. Math.**35**(1983), no. 1, 145–166. MR**685822**, 10.4153/CJM-1983-010-7**[3]**A. Bellow and V. Losert,*On sequences of density zero in ergodic theory*, Conference in modern analysis and probability (New Haven, Conn., 1982), Contemp. Math., vol. 26, Amer. Math. Soc., Providence, RI, 1984, pp. 49–60. MR**737387**, 10.1090/conm/026/737387**[4]**A. Bellow and V. Losert,*The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences*, Trans. Amer. Math. Soc.**288**(1985), no. 1, 307–345. MR**773063**, 10.1090/S0002-9947-1985-0773063-8**[5]**J. Bourgain,*On the maximal ergodic theorem for certain subsets of the integers*, Israel J. Math.**61**(1988), no. 1, 39–72. MR**937581**, 10.1007/BF02776301**[6]**J. Bourgain,*An approach to pointwise ergodic theorems*, Geometric aspects of functional analysis (1986/87), Lecture Notes in Math., vol. 1317, Springer, Berlin, 1988, pp. 204–223. MR**950982**, 10.1007/BFb0081742**[7]**J. Bourgain,*On the pointwise ergodic theorem on 𝐿^{𝑝} for arithmetic sets*, Israel J. Math.**61**(1988), no. 1, 73–84. MR**937582**, 10.1007/BF02776302**[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), 349–353. MR**0227354****[10]**Alberto de la Torre,*A simple proof of the maximal ergodic theorem*, Canad. J. Math.**28**(1976), no. 5, 1073–1075. MR**0417819****[11]**Roger L. Jones,*Necessary and sufficient conditions for a maximal ergodic theorem along subsequences*, Ergodic Theory Dynam. Systems**7**(1987), no. 2, 203–210. MR**896793**, 10.1017/S0143385700003953**[12]**Roger L. Jones and James Olsen,*Subsequence pointwise ergodic theorems for operators in 𝐿^{𝑝}*, Israel J. Math.**77**(1992), no. 1-2, 33–54. MR**1194784**, 10.1007/BF02808009**[13]**Charn Huen Kan,*Ergodic properties of Lamperti operators*, Canad. J. Math.**30**(1978), no. 6, 1206–1214. MR**511557**, 10.4153/CJM-1978-100-x**[14]**John Lamperti,*On the isometries of certain function-spaces*, Pacific J. Math.**8**(1958), 459–466. MR**0105017****[15]**James Olsen,*Dominated estimates of convex combinations of commuting isometries*, Israel J. Math.**11**(1972), 1–13. MR**0302862****[16]**James H. Olsen,*The individual ergodic theorem for Lamperti contractions*, C. R. Math. Rep. Acad. Sci. Canada**3**(1981), no. 2, 113–118. MR**612399****[17]**Máté Wierdl,*Pointwise ergodic theorem along the prime numbers*, Israel J. Math.**64**(1988), no. 3, 315–336 (1989). MR**995574**, 10.1007/BF02882425

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1043860-6

Keywords:
Subsequences,
positive contractions,
Lamperti operators

Article copyright:
© Copyright 1992
American Mathematical Society