A perturbed ergodic theorem
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- by Radu-Nicolae Gologan PDF
- Proc. Amer. Math. Soc. 128 (2000), 1377-1380 Request permission
Abstract:
Using a version of an ergodic lemma due to Cuculescu and Foiaş, we prove a pointwise ergodic theorem for $L^1$-contractions which can be viewed as a perturbed version of the celebrated ergodic theorem of Chacon and Ornstein. Surprisingly, to some extent, the complex part of the iterates involved have no effect on the ergodic convergence.References
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- R. V. Chacon and D. S. Ornstein, A general ergodic theorem, Illinois J. Math. 4 (1960), 153–160. MR 110954, DOI 10.1215/ijm/1255455860
- I. Cuculescu and C. Foiaş, An individual ergodic theorem for positive operators, Rev. Roumaine Math. Pures Appl. 11 (1966), 581–594. MR 199348
- Radu-Nicolae Gologan, An extension of Chacon-Ornstein ergodic theorem, Invariant subspaces and other topics (Timişoara/Herculane, 1981), Operator Theory: Advances and Applications, vol. 6, Birkhäuser, Basel-Boston, Mass., 1982, pp. 75–80. MR 685455
- Ulrich Krengel, Ergodic theorems, De Gruyter Studies in Mathematics, vol. 6, Walter de Gruyter & Co., Berlin, 1985. With a supplement by Antoine Brunel. MR 797411, DOI 10.1515/9783110844641
Additional Information
- Radu-Nicolae Gologan
- Affiliation: Institutul de Matematică al Academiei Române, CP 1-764, 70700 Bucureşti, România
- Email: rgologan@stoilow.imar.ro
- Received by editor(s): June 23, 1998
- Published electronically: August 17, 1999
- Additional Notes: The author was partially supported by the Romanian Academy, grant GAR 6645
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1377-1380
- MSC (1991): Primary 47A35, 28D99
- DOI: https://doi.org/10.1090/S0002-9939-99-05243-0
- MathSciNet review: 1653465