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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
DOI: https://doi.org/10.1090/S0002-9939-99-05243-0
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?)

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  • 2. R.V. CHACON, D.S. ORNSTEIN: A general ergodic theorem, Ill. J. Math., 4, 1960, pp. 153-160. MR 22:1822
  • 3. C. CUCULESCU, C. FOIAS: An individual ergodic theorem for positive operators, Rev. Roum. Math. Pures et Appl., Tome XI, 1966, pp. 581-594. MR 33:7495
  • 4. R.-N. GOLOGAN: An extension of Chacon-Ornstein ergodic theorem, in Invariant Subspaces and other Topics, Birkhäuser Verlag, 1982, pp. 75-80. MR 84m:47014
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Additional Information

Radu-Nicolae Gologan
Affiliation: Institutul de Matematică al Academiei Române, CP 1-764, 70700 Bucureşti, România
Email: rgologan@stoilow.imar.ro

DOI: https://doi.org/10.1090/S0002-9939-99-05243-0
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