Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2023, Volume: 20, Number: 1, Pages: 183-206 Pages count : 24 DOI: 10.33048/semi.2023.20.016 | ||||
| Tags | von Neumann's ergodic theorem; rates 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:
Power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in von Neumann's ergodic theorem with continuous time is considered. All possible exponents of the considered power-law convergence are found; for each of these exponents, spectral criteria for such convergence are given and a complete description of all such subspaces is obtained. Uniform convergence over the entire space takes place only in trivial cases, which explains the interest in the uniform convergence just on subspaces. In addition, along the way, the old convergence rate estimates in the von Neumann ergodic theorem for (semi) ows are generalized and refined.
Cite:
Kachurovskii A.G.
, Podvigin I.V.
, Todikov V.E.
Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N1. P.183-206. DOI: 10.33048/semi.2023.20.016 WOS Scopus РИНЦ MathNet
Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N1. P.183-206. DOI: 10.33048/semi.2023.20.016 WOS Scopus РИНЦ MathNet
Dates:
| Submitted: | Jul 3, 2022 |
| Published print: | Mar 1, 2023 |
| Published online: | Mar 1, 2023 |
Identifiers:
| Web of science: | WOS:000959070400010 |
| Scopus: | 2-s2.0-85150798440 |
| Elibrary: | 54768288 |
| MathNet: | semr1580 |