Author:
Herzog Gerd,Kunstmann Peer
Abstract
AbstractFor an element a of a Banach algebra (scaled to spectral radius 1) we prove that the spectral radius is contained in the spectrum, if the sequence of powers $$(a^k)$$
(
a
k
)
is asymptotically not too far from a normal cone.
Funder
Karlsruher Institut für Technologie (KIT)
Publisher
Springer Science and Business Media LLC
Reference10 articles.
1. Aupetit, B.: A Primer on Spectral Theory. Universitext. Springer-Verlag, New York (1991)
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, 424–440 (2019)
3. Dixmier J.: $$C^\ast $$-algebras. North-Holland Math. Library, Vol. 15 North-Holland Publishing Co., Amsterdam-New York-Oxford, (1977)
4. Glück, J.: Towards a Perron–Frobenius theory for eventually positive operators. J. Math. Anal. Appl. 453, 317–337 (2017)
5. Herzog, G., Kunstmann, P.: Eventually positive elements in ordered Banach algebras. Comment. Math. Univ. Carolin. 64, 321–330 (2023)