On a convergence theorem for semigroups of positive integral operators
- We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result.
| Author details: | Moritz Reinhardt GerlachORCiDGND, Jochen Glück |
|---|---|
| DOI: | https://doi.org/10.1016/j.crma.2017.07.017 |
| ISSN: | 1631-073X |
| ISSN: | 1778-3569 |
| Title of parent work (English): | Comptes Rendus Mathematique |
| Publisher: | Elsevier |
| Place of publishing: | Paris |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2017/09/06 |
| Publication year: | 2017 |
| Release date: | 2022/01/21 |
| Volume: | 355 |
| Number of pages: | 4 |
| First page: | 973 |
| Last Page: | 976 |
| 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 / Bronze Open-Access |
