Desheng Li, Ruijing Wang, Luyan Zhou
Published 2022-07-16Version 1
In this note we present some generalized versions of the Krein-Rutman theorem for sectorial operators. They are formulated in a fashion that can be easily applied to elliptic operators. Another feature of these generalized versions is that they contain some information on the generalized eigenspaces associated with non-principal eigenvalues, which are helpful in the study of the dynamics of evolution equations in ordered Banach spaces.
A counterexample to a nonlinear version of the Krein-Rutman theorem by R. Mahadevan
Regularity Properties of Sectorial Operators: Counterexamples and Open Problems
New properties of the multivariable $H^\infty$ functional calculus of sectorial operators
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