Measure-preserving semiflows and one-parameter Koopman semigroups
- For a finite measure space X, we characterize strongly continuous Markov lattice semigroups on Lp(X) by showing that their generator A acts as a derivation on the dense subspace D(A)L(X). We then use this to characterize Koopman semigroups on Lp(X) if X is a standard probability space. In addition, we show that every measurable and measure-preserving flow on a standard probability space is isomorphic to a continuous flow on a compact Borel probability space.
Author details: | Nikolai Edeko, Moritz Reinhardt GerlachORCiDGND, Viktoria KühnerORCiDGND |
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DOI: | https://doi.org/10.1007/s00233-018-9960-3 |
ISSN: | 0037-1912 |
ISSN: | 1432-2137 |
Title of parent work (English): | Semigroup forum |
Publisher: | Springer |
Place of publishing: | New York |
Publication type: | Article |
Language: | English |
Date of first publication: | 2019/08/06 |
Publication year: | 2019 |
Release date: | 2021/04/14 |
Tag: | Derivation; Koopman semigroup; Measure-preserving semiflow; Topological model |
Volume: | 98 |
Issue: | 1 |
Number of pages: | 16 |
First page: | 48 |
Last Page: | 63 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |