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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 |
|---|---|
| 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 |
