A random ergodic theorem in von Neumann algebras

Dang Ngoc, Nghiem

doi:10.1090/S0002-9939-1982-0674090-4

A random ergodic theorem in von Neumann algebras
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by Nghiem Dang Ngoc

Proc. Amer. Math. Soc. 86 (1982), 605-608

DOI: https://doi.org/10.1090/S0002-9939-1982-0674090-4

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Abstract:

E. C. Lance has recently extended the Birkhoff ergodic theorem to noncommutative dynamical systems. Using Lance’s result, we extend the random ergodic theorem of H. R. Pitt, S. M. Ulam, S. Kakutani and J. von Neumann to noncommutative context.

References

J.-P. Conze and N. Dang-Ngoc, Ergodic theorems for noncommutative dynamical systems, Invent. Math. 46 (1978), no. 1, 1–15. MR 500185, DOI 10.1007/BF01390100
Nghiêm Đặng Ngọc, Pointwise convergence of martingales in von Neumann algebras, Israel J. Math. 34 (1979), no. 4, 273–280 (1980). MR 570886, DOI 10.1007/BF02760608

Les algèbres d’opérateurs dans l’espace hilbertien

Shizuo Kakutani, Random ergodic theorems and Markoff processes with a stable distribution, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley-Los Angeles, Calif., 1951, pp. 247–261. MR 0044773
E. Christopher Lance, Ergodic theorems for convex sets and operator algebras, Invent. Math. 37 (1976), no. 3, 201–214. MR 428060, DOI 10.1007/BF01390319
E. Christopher Lance, Martingale convergence in von Neumann algebras, Math. Proc. Cambridge Philos. Soc. 84 (1978), no. 1, 47–56. MR 489568, DOI 10.1017/S0305004100054864
H. R. Pitt, Some generalizations of the ergodic theorem, Proc. Cambridge Philos. Soc. 38 (1942), 325–343. MR 7947, DOI 10.1017/S0305004100022027
C. Ryll-Nardzewski, On the ergodic theorems. III. The random ergodic theorem, Studia Math. 14 (1954), 298–301 (1955). MR 68611, DOI 10.4064/sm-14-2-298-301
Françoise Ulam, Nonmathematical reminiscences about Johnny von Neumann, The legacy of John von Neumann (Hempstead, NY, 1988) Proc. Sympos. Pure Math., vol. 50, Amer. Math. Soc., Providence, RI, 1990, pp. 9–13. MR 1067746, DOI 10.1090/pspum/050/1067746