Geodesic
Eventually positive elements in ordered Banach algebras
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 3, pp. 321-330.

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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.
DOI : 10.14712/1213-7243.2023.030
Classification : 46B40, 46H05
Keywords: ordered Banach algebra; eventually positive element; spectral property; Perron--Frobenius property 
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Herzog, Gerd; Kunstmann, Peer C. Eventually positive elements in ordered Banach algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 3, pp. 321-330. doi : 10.14712/1213-7243.2023.030. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.030/

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