Abstract
Recently, E.C. Lance extended the pointwise ergodic theorem to actions of the group of integers on von Neumann algebras. Our purpose is to extend other pointwise ergodic theorems to von Neumann algebra context: the Dunford-Schwartz-Zygmund pointwise ergodic theorem, the pointwise ergodic theorem for connected amenable locally compact groups, the Wiener's local ergodic theorem for ℝ d+ and for general Lie groups.
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Conze, J.P., Dang-Ngoc, N. Ergodic theorems for noncommutative dynamical systems. Invent Math 46, 1–15 (1978). https://doi.org/10.1007/BF01390100
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DOI: https://doi.org/10.1007/BF01390100