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

Adam Kanigowski; Wojciech Kryszewski

Open Mathematics (2012)

  • Volume: 10, Issue: 6, page 2240-2263
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Adam Kanigowski, and Wojciech Kryszewski. "Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators." Open Mathematics 10.6 (2012): 2240-2263. <http://eudml.org/doc/269599>.

@article{AdamKanigowski2012,
abstract = {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.},
author = {Adam Kanigowski, Wojciech Kryszewski},
journal = {Open Mathematics},
keywords = {Eigenvalue; Eigenvector; Spectral bound; Essential spectrum; Positive operators; Tangent cone; Tangency condition; Perron-Frobenius theorem; Krein-Rutman theorem; Strongly continuous semigroup; eigenvalue; eigenvector; spectral bound; essential spectrum; positive operators; tangent cone; tangency condition; strongly continuous semigroup},
language = {eng},
number = {6},
pages = {2240-2263},
title = {Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators},
url = {http://eudml.org/doc/269599},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Adam Kanigowski
AU - Wojciech Kryszewski
TI - Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators
JO - Open Mathematics
PY - 2012
VL - 10
IS - 6
SP - 2240
EP - 2263
AB - 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.
LA - eng
KW - Eigenvalue; Eigenvector; Spectral bound; Essential spectrum; Positive operators; Tangent cone; Tangency condition; Perron-Frobenius theorem; Krein-Rutman theorem; Strongly continuous semigroup; eigenvalue; eigenvector; spectral bound; essential spectrum; positive operators; tangent cone; tangency condition; strongly continuous semigroup
UR - http://eudml.org/doc/269599
ER -

References

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