Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time Full article
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Mathematical Notes
ISSN: 0001-4346 , E-ISSN: 1573-8876 |
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| Output data | Year: 2023, Volume: 113, Number: 5, Pages: 680–693 Pages count : 14 DOI: 10.1134/S0001434623050073 | ||||
| Tags | von Neumann ergodic theorem , rate of convergence in ergodic theorems, power-law uniform convergence | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
We consider the power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in the von Neumann ergodic theorem with discrete time. All possible exponents of the considered power-law convergence are found; for each of these exponents, spectral criteria for such convergence are given and the complete description of all such subspaces is obtained. Uniform convergence on the whole space takes place only in the trivial cases, which explains the interest in uniform convergence precisely on subspaces. In addition, by the way, old estimates of the rates of convergence in the von Neumann ergodic theorem for measure-preserving mappings are generalized and refined.
Cite:
Kachurovskii A.G.
, Podvigin I.V.
, Khakimbaev A.Z.
Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time
Mathematical Notes. 2023. V.113. N5. P.680–693. DOI: 10.1134/S0001434623050073 WOS Scopus РИНЦ OpenAlex
Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time
Mathematical Notes. 2023. V.113. N5. P.680–693. DOI: 10.1134/S0001434623050073 WOS Scopus РИНЦ OpenAlex
Original:
Качуровский А.Г.
, Подвигин И.В.
, Хакимбаев А.Ж.
Равномерная сходимость на подпространствах в эргодической теореме фон Неймана с дискретным временем
Математические заметки. 2023. Т.113. №5. С.713–730. DOI: 10.4213/mzm13739 РИНЦ MathNet OpenAlex
Равномерная сходимость на подпространствах в эргодической теореме фон Неймана с дискретным временем
Математические заметки. 2023. Т.113. №5. С.713–730. DOI: 10.4213/mzm13739 РИНЦ MathNet OpenAlex
Dates:
| Submitted: | Sep 26, 2022 |
| Accepted: | Dec 12, 2022 |
| Published print: | Jun 8, 2023 |
| Published online: | Jun 8, 2023 |
Identifiers:
| Web of science: | WOS:001016366900007 |
| Scopus: | 2-s2.0-85163150206 |
| Elibrary: | 61894013 |
| OpenAlex: | W4381331245 |