Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators

• Autorzy: Adam Kanigowski , Wojciech Kryszewski
• Języki publikacji: EN

Abstrakty

EN

We study several aspects of a generalized Perron-Frobenius and Krein-Rutman theorems concerning spectral properties of a (possibly unbounded) linear operator on a cone in a Banach space. The operator is subject to the so-called tangency or weak range assumptions implying the resolvent invariance of the cone. The further assumptions rely on relations between the spectral and essential spectral bounds of the operator. In general we do not assume that the cone induces the Banach lattice structure into the underlying space.

Słowa kluczowe

EN

Eigenvalue; Eigenvector; Spectral bound; Essential spectrum; Positive operators; Tangent cone; Tangency condition; Perron-Frobenius theorem; Krein-Rutman theorem; Strongly continuous semigroup

Kategorie tematyczne

• 47D03: Groups and semigroups of linear operators
• 15A18: Eigenvalues, singular values, and eigenvectors
• 47A75: Eigenvalue problems
• 47A10: Spectrum, resolvent

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 2240-2263

Daty

wydano

2012-12-01

online

2012-10-12

Twórcy

autor

Adam Kanigowski

• Faculty of Mathematics and Computer Sciences, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland

autor

Wojciech Kryszewski

• Faculty of Mathematics and Computer Sciences, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland

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Identyfikatory

DOI

10.2478/s11533-012-0118-3