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A perturbed ergodic theorem

Author: Radu-Nicolae Gologan
Journal: Proc. Amer. Math. Soc. 128 (2000), 1377-1380
MSC (1991): Primary 47A35, 28D99
Published electronically: August 17, 1999
MathSciNet review: 1653465
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Abstract | References | Similar Articles | Additional Information

Abstract: Using a version of an ergodic lemma due to Cuculescu and Foias, 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 [Enhancements On Off] (What's this?)

  • 1. R. V. Chacon, Convergence of operator averages, Ergodic Theory (Proc. Internat. Sympos., Tulane Univ., New Orleans, La., 1961) Academic Press, New York, 1963, pp. 89–120. MR 0160872
  • 2. R. V. Chacon and D. S. Ornstein, A general ergodic theorem, Illinois J. Math. 4 (1960), 153–160. MR 0110954
  • 3. I. Cuculescu and C. Foiaş, An individual ergodic theorem for positive operators, Rev. Roumaine Math. Pures Appl. 11 (1966), 581–594. MR 0199348
  • 4. Radu-Nicolae Gologan, An extension of Chacon-Ornstein ergodic theorem, Invariant subspaces and other topics (Timişoara/Herculane, 1981), Operator Theory: Adv. Appl., vol. 6, Birkhäuser, Basel-Boston, Mass., 1982, pp. 75–80. MR 685455
  • 5. 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

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Additional Information

Radu-Nicolae Gologan
Affiliation: Institutul de Matematică al Academiei Române, CP 1-764, 70700 Bucureşti, România

Keywords: $L^1$-contraction, ergodic theorem
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
Article copyright: © Copyright 2000 American Mathematical Society