  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.

Functional Analysis