A note on the Krein–Rutman theorem for sectorial operators

Abstract

In this paper, 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 nonprincipal eigenvalues, which are helpful in the study of the dynamics of evolution equations in ordered Banach spaces.