Previous |  Up |  Next

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
.
Category: math
.
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
.
Date available: 2024-03-18T10:42:01Z
Last updated: 2024-08-02
Stable URL: http://hdl.handle.net/10338.dmlcz/152301
.
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
.

Fulltext not available (moving wall 24 months)

Partner of
EuDML logo