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Mathematics > Operator Algebras

arXiv:2206.12228 (math)
[Submitted on 24 Jun 2022]

Title:Noncommutative maximal ergodic inequalities for amenable groups

Authors:Léonard Cadilhac, Simeng Wang
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Abstract:We prove a pointwise ergodic theorem for actions of amenable groups on noncommutative measure spaces. To do so, we establish the maximal ergodic inequality for averages of operator-valued functions on amenable groups. The main arguments are a geometric construction of martingales based on the Ornstein-Weiss quasi-tilings and harmonic analytic estimates coming from noncommutative Calderón-Zygmund theory.
Comments: Preliminary version, comments are welcome. 22 pages
Subjects: Operator Algebras (math.OA); Dynamical Systems (math.DS); Functional Analysis (math.FA); Group Theory (math.GR)
Cite as: arXiv:2206.12228 [math.OA]
  (or arXiv:2206.12228v1 [math.OA] for this version)
  https://doi.org/10.48550/arXiv.2206.12228

Submission history

From: Léonard Cadilhac [view email]
[v1] Fri, 24 Jun 2022 11:54:02 UTC (27 KB)
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