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

Adam Kanigowski, Wojciech Kryszewski
2012 Open Mathematics  
AbstractWe 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
more » ... e Banach lattice structure into the underlying space.
doi:10.2478/s11533-012-0118-3 fatcat:tufs7ttk2vadrgob3r2srwfyfa