Convergence of positive operator semigroups
- We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter.
Author details: | Moritz Reinhardt GerlachORCiDGND, Jochen GlückORCiDGND |
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DOI: | https://doi.org/10.1090/tran/7836 |
ISSN: | 0002-9947 |
ISSN: | 1088-6850 |
Title of parent work (English): | Transactions of the American Mathematical Society |
Publisher: | American Mathematical Soc. |
Place of publishing: | Providence |
Publication type: | Article |
Language: | English |
Year of first publication: | 2019 |
Publication year: | 2019 |
Release date: | 2020/10/06 |
Tag: | Positive semigroups; asymptotic behavior; kernel operator; semigroup representations |
Volume: | 372 |
Issue: | 9 |
Number of pages: | 25 |
First page: | 6603 |
Last Page: | 6627 |
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 |
Open Access / Green Open-Access |