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)

 
 

 

On the individual ergodic theorem for positive operators


Author: Ryōtarō Satō
Journal: Proc. Amer. Math. Soc. 36 (1972), 456-458
MSC: Primary 47A35; Secondary 28A65
DOI: https://doi.org/10.1090/S0002-9939-1972-0308820-1
MathSciNet review: 0308820
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A theorem which gives a condition on a positive linear contraction on an $ {L^1}$-space in order that the individual ergodic theorem hold is proved. The theorem contains a result obtained by Y. Ito as a special case.


References [Enhancements On Off] (What's this?)

  • [1] M. A. Akcoglu and R. V. Chacon, A convexity theorem for positive operators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1965), 328-332. MR 32 #192. MR 0182710 (32:192)
  • [2] G. Baxter, A general ergodic theorem with weighted averages, J. Math. Mech. 14 (1965), 277-288. MR 30 #4904. MR 0174704 (30:4904)
  • [3] R. V. Chacon, Identification of the limit of operator averages, J. Math. Mech. 11 (1962), 961-968. MR 26 #2883. MR 0145352 (26:2883)
  • [4] R. V. Chacon and D. S. Ornstein, A general ergodic theorem, Illinois J. Math. 4 (1960), 153-160. MR 22 #1822. MR 0110954 (22:1822)
  • [5] L. W. Cohen, On the mean ergodic theorem, Ann. of Math. (2) 41 (1940), 505-509. MR 0002027 (1:339b)
  • [6] Y. Ito, Uniform integrability and the pointwise ergodic theorem, Proc. Amer. Math. Soc. 16 (1965), 222-227. MR 30 #2121. MR 0171895 (30:2121)
  • [7] R. Sato, On a general ratio ergodic theorem with weighted averages, Proc. Amer. Math. Soc. 35 (1972), 177-178. MR 0303317 (46:2455)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A35, 28A65

Retrieve articles in all journals with MSC: 47A35, 28A65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0308820-1
Keywords: Positive linear contraction, individual ergodic theorem, weak sequential compactness
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society