On the Bonsall cone spectral radius and the approximate point spectrum

0476010 - MÚ 2018 RIV US eng J - Článek v odborném periodiku
Müller, Vladimír - Peperko, A.
On the Bonsall cone spectral radius and the approximate point spectrum.
Discrete and Continuous Dynamical Systems. Roč. 37, č. 10 (2017), s. 5337-5354. ISSN 1078-0947. E-ISSN 1553-5231
Grant CEP: GA ČR(CZ) GA17-00941S
Institucionální podpora: RVO:67985840
Klíčová slova: Bonsall's cone spectral radius * local spectral radii * approximate point spectrum
Obor OECD: Pure mathematics
Impakt faktor: 1.126, rok: 2017
http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=14323

We study the Bonsall cone spectral radius and the approximate point spectrum of (in general non-linear) positively homogeneous, bounded and supremum preserving maps, defined on a max-cone in a given normed vector lattice. We prove that the Bonsall cone spectral radius of such maps is always included in its approximate point spectrum. Moreover, the approximate point spectrum always contains a (possibly trivial) interval. Our results apply to a large class of (nonlinear) max-type operators. We also generalize a known result that the spectral radius of a positive (linear) operator on a Banach lattice is contained in the approximate point spectrum. Under additional generalized compactness type assumptions our results imply Krein-Rutman type results.
Trvalý link: http://hdl.handle.net/11104/0272582