Mean ergodicity vs weak almost periodicity
- We provide explicit examples of positive and power-bounded operators on c(0) and l(infinity) which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature. Finally, we prove that if T is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of T .
| Author details: | Moritz Reinhardt GerlachORCiDGND, Jochen GlückORCiDGND |
|---|---|
| DOI: | https://doi.org/10.4064/sm170918-20-3 |
| ISSN: | 0039-3223 |
| ISSN: | 1730-6337 |
| Title of parent work (English): | Studia mathematica |
| Publisher: | Polska Akademia Nauk, Instytut Matematyczny |
| Place of publishing: | Warszawa |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2019/02/22 |
| Publication year: | 2019 |
| Release date: | 2021/05/17 |
| Tag: | KB-space; mean ergodic; order continuous norm; positive operators; weakly almost periodic |
| Volume: | 248 |
| Issue: | 1 |
| Number of pages: | 12 |
| First page: | 45 |
| Last Page: | 56 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
