Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF

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, Proc.Internat. Sympos. Ergodic Theory, Academic Press, New York 1963, 89-120. MR 28:4081
  • 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
  • 5. U.KRENGEL: Ergodic Theorems, Walter de Gruyter, Berlin; New York, 1985. MR 87i:28001

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A35, 28D99

Retrieve articles in all journals with MSC (1991): 47A35, 28D99

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