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 |
| DOI: | 10.14712/1213-7243.2023.030 |
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| Date available: | 2024-03-18T10:42:01Z |
| Last updated: | 2024-03-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152301 |
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| Reference: | [1] Bonsall F. F., Duncan J.: Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras.London Math. Soc. Lecture Note Ser., 2, Cambridge University Press, London, 1971. MR 0288583 |
| Reference: | [2] Chaysri T., Noutsos D.: On the Perron–Frobenius theory of $M_v$-matrices and equivalent properties to eventually exponentially nonnegative matrices.Electron. J. Linear Algebra 35 (2019), 424–440. MR 4023015, 10.13001/ela.2019.5241 |
| Reference: | [3] Glück J.: Towards a Perron–Frobenius theory for eventually positive operators.J. Math. Anal. Appl. 453 (2017), no. 1, 317–337. MR 3641777, 10.1016/j.jmaa.2017.03.071 |
| Reference: | [4] Mouton S.: A spectral problem in ordered Banach algebras.Bull. Austral. Math. Soc. 67 (2003), no. 1, 131–144. MR 1962967, 10.1017/S0004972700033591 |
| Reference: | [5] Mouton S., Raubenheimer H.: More spectral theory in ordered Banach algebras.Positivity 1 (1997), no. 4, 305–317. MR 1660397, 10.1023/A:1009717500980 |
| Reference: | [6] Raubenheimer H., Rode S.: Cones in Banach algebras.Indag. Math. (N.S.) 7 (1996), no. 4, 489–502. MR 1620116, 10.1016/S0019-3577(97)89135-5 |
| Reference: | [7] Shakeri F., Alizadeh R.: Nonnegative and eventually positive matrices.Linear Algebra Appl. 519 (2017), 19–26. MR 3606259 |
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