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

被引：6

作者：

Kanigowski, Adam ^{[1
]}

Kryszewski, Wojciech ^{[1
]}

机构：

[1] Nicolaus Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2012年 / 10卷 / 06期

关键词：

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

D O I：

10.2478/s11533-012-0118-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：2240 / 2263

页数：24

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