On the Bonsall cone spectral radius and the approximate point spectrum

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00476010" target="_blank" >RIV/67985840:_____/17:00476010 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.3934/dcds.2017232" target="_blank" >http://dx.doi.org/10.3934/dcds.2017232</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcds.2017232" target="_blank" >10.3934/dcds.2017232</a>

Result language
angličtina
Original language name
On the Bonsall cone spectral radius and the approximate point spectrum
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-00941S" target="_blank" >GA17-00941S: Topological and geometrical properties of Banach spaces and operator algebras II</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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