An ergodic theorem for noncommutative operators
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- by Takeshi Yoshimoto
- Proc. Amer. Math. Soc. 54 (1976), 125-129
- DOI: https://doi.org/10.1090/S0002-9939-1976-0407625-4
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Abstract:
This note contains a proof of a weighted convergence theorem which includes the ordinary “noncommuting” ergodic theorem for noncommutative families of linear contraction operators.References
- M. A. Akcoglu and R. V. Chacon, A convexity theorem for positive operators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1965), 328–332 (1965). MR 182710, DOI 10.1007/BF00535783
- Glen Baxter, An ergodic theorem with weighted averages, J. Math. Mech. 13 (1964), 481–488. MR 0165070
- Glen Baxter, A general ergodic theorem with weighted averages, J. Math. Mech. 14 (1965), 277–288. MR 0174704
- R. V. Chacon, Ordinary means imply recurrent means, Bull. Amer. Math. Soc. 70 (1964), 796–797. MR 168720, DOI 10.1090/S0002-9904-1964-11240-4
- Nelson Dunford, An individual ergodic theorem for non-commutative transformations, Acta Sci. Math. (Szeged) 14 (1951), 1–4. MR 42074
- Nelson Dunford and J. T. Schwartz, Convergence almost everywhere of operator averages, J. Rational Mech. Anal. 5 (1956), 129–178. MR 77090, DOI 10.1512/iumj.1956.5.55003
- D. L. Hanson and Gordon Pledger, On the mean ergodic theorem for weighted averages, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 141–149. MR 254214, DOI 10.1007/BF00537020
- Takeshi Yoshimoto, Random ergodic theorem with weighted averages, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 30 (1974), 149–165; erratum, ibid. 31 (1974/75), 161. MR 364601, DOI 10.1007/BF00532267 —, Induced contraction semigroups and random ergodic theorems, Dissertationes Math. (to appear).
- A. Zygmund, An individual ergodic theorem for non-commutative transformations, Acta Sci. Math. (Szeged) 14 (1951), 103–110. MR 45948
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 125-129
- MSC: Primary 47A35
- DOI: https://doi.org/10.1090/S0002-9939-1976-0407625-4
- MathSciNet review: 0407625