Noncommutative maximal ergodic inequalities for amenable groups
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866908506617020416 |
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| author | Cadilhac, Léonard Wang, Simeng |
| author_facet | Cadilhac, Léonard Wang, Simeng |
| contents | We prove a pointwise ergodic theorem and a maximal inequality for actions of amenable groups on noncommutative measure spaces. To do so, we establish a square function estimate quantifying the difference between ergodic averages and some conditional expectations. Our main technical results are the construction of a well-behaved filtration, based on the quasi-tilings of Ornstein and Weiss, and the square function bound, which we derive from non-doubling noncommutative Calderón-Zygmund decomposition. For actions on usual measure spaces, we obtain new variational ergodic inequalities and jump estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12228 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Noncommutative maximal ergodic inequalities for amenable groups Cadilhac, Léonard Wang, Simeng Operator Algebras Dynamical Systems Functional Analysis Group Theory We prove a pointwise ergodic theorem and a maximal inequality for actions of amenable groups on noncommutative measure spaces. To do so, we establish a square function estimate quantifying the difference between ergodic averages and some conditional expectations. Our main technical results are the construction of a well-behaved filtration, based on the quasi-tilings of Ornstein and Weiss, and the square function bound, which we derive from non-doubling noncommutative Calderón-Zygmund decomposition. For actions on usual measure spaces, we obtain new variational ergodic inequalities and jump estimates. |
| title | Noncommutative maximal ergodic inequalities for amenable groups |
| topic | Operator Algebras Dynamical Systems Functional Analysis Group Theory |
| url | https://arxiv.org/abs/2206.12228 |