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 -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.

**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

Email:
rgologan@stoilow.imar.ro

DOI:
http://dx.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