Lower spectral radius and spectral mapping theorem for suprema preserving mappings

0490357 - MÚ 2019 RIV US eng J - Článek v odborném periodiku
Müller, Vladimír - Peperko, A.
Lower spectral radius and spectral mapping theorem for suprema preserving mappings.
Discrete and Continuous Dynamical Systems. Roč. 38, č. 8 (2018), s. 4117-4132. ISSN 1078-0947. E-ISSN 1553-5231
Grant CEP: GA ČR GA17-00941S
Institucionální podpora: RVO:67985840
Klíčová slova: spectral mapping theorem * approximate point spectrum * Bonsall's cone spectral radius
Obor OECD: Pure mathematics
Impakt faktor: 1.143, rok: 2018
http://aimsciences.org//article/doi/10.3934/dcds.2018179

We study Lipschitz, positively homogeneous and finite suprema preserving mappings defined on a max-cone of positive elements in a normed vector lattice. We prove that the lower spectral radius of such a mapping is always a minimum value of its approximate point spectrum. We apply this result to show that the spectral mapping theorem holds for the approximate point spectrum of such a mapping. By applying this spectral mapping theorem we obtain new inequalites for the Bonsall cone spectral radius of max-type kernel operators.
Trvalý link: http://hdl.handle.net/11104/0284610