Article
| Title: | Eventually positive elements in ordered Banach algebras (English) |
| Author: | Herzog, Gerd |
| Author: | Kunstmann, Peer C. |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 3 |
| Year: | 2023 |
| Pages: | 321-330 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | In ordered Banach algebras, we introduce eventually and asymptotically positive elements. We give conditions for the following spectral properties: the spectral radius belongs to the spectrum (Perron--Frobenius property); the spectral radius is the only element in the peripheral spectrum; there are positive (approximate) eigenvectors for the spectral radius. Recently such types of results have been shown for operators on Banach lattices. Our results can be viewed as a complement, since our structural assumptions on the ordered Banach algebra are much weaker. (English) |
| Keyword: | ordered Banach algebra |
| Keyword: | eventually positive element |
| Keyword: | spectral property |
| Keyword: | Perron--Frobenius property |
| MSC: | 46B40 |
| MSC: | 46H05 |
| idZBL: | Zbl 07830511 |
| idMR: | MR4717504 |
| DOI: | 10.14712/1213-7243.2023.030 |
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| Date available: | 2024-03-18T10:42:01Z |
| Last updated: | 2024-08-02 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152301 |
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