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An abelian ergodic theorem for semigroups in $ L\sb{p}$ space


Author: S. A. McGrath
Journal: Proc. Amer. Math. Soc. 54 (1976), 231-236
DOI: https://doi.org/10.1090/S0002-9939-1976-0394250-7
MathSciNet review: 0394250
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Abstract | References | Additional Information

Abstract: The purpose of this paper is to prove individual and dominated ergodic theorems for Abel means of semigroups of positive $ {L_p}$ contractions, $ 1 < p < \infty $.


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

  • [1] M. A. Akcoglu, A pointwise ergodic theorem in $ {L_p}$ spaces, Canad. J. Math. (to appear). MR 0396901 (53:761)
  • [2] R. V. Chacón and J. Olsen, Dominated estimates of positive contractions, Proc. Amer. Math. Soc. 20 (1969), 266-271. MR 40 #1579. MR 0248327 (40:1579)
  • [3] N. Dunford and J. T. Schwartz, Linear operators. I. General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [4] P. R. Halmos, Lectures on ergodic theory, Publ. Math. Soc. Japan, no. 3, Math. Soc. of Japan, Tokyo, 1956; reprint, Chelsea, New York, 1960. MR 20 #3958; 22 #2677. MR 0097489 (20:3958)
  • [5] A. Ionescu Tulcea, Ergodic properties of isometries in $ {L^p}$ spaces, $ 1 < p < \infty $, Bull. Amer. Math. Soc. 70 (1964), 366-371. MR 34 #6026. MR 0206207 (34:6026)
  • [6] J. Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), 459-466. MR 21 #3764. MR 0105017 (21:3764)
  • [7] R. Sato, An Abel-maximal ergodic theorem for semigroups, Pacific J. Math. 51 (1974), 543-547. MR 0370225 (51:6454)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0394250-7
Keywords: Abel mean, individual ergodic theorem, strongly continuous semigroup, positive $ {L_p}$ contraction
Article copyright: © Copyright 1976 American Mathematical Society

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