TY - JOUR
T1 - Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators
AU - Kanigowski, Adam
AU - Kryszewski, Wojciech
N1 - Funding Information:
The second author was supported by Polish Ministry of Higher Education Grant nr N N 201 395137.
PY - 2012
Y1 - 2012
N2 - 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.
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.
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U2 - 10.2478/s11533-012-0118-3
DO - 10.2478/s11533-012-0118-3
M3 - Article
AN - SCOPUS:84867448073
SN - 1895-1074
VL - 10
SP - 2240
EP - 2263
JO - Central European Journal of Mathematics
JF - Central European Journal of Mathematics
IS - 6
ER -