Extensions of operators leaving the spectrum invariant (Q1340594)

The aim of this paper is to compare operators not defined on the same space. It is a common situation that operators are defined on different spaces, but they can naturally be considered ``close'' to each other. To examine such a situation, the operators have to be extended into a space different from the original without changing the vital properties of these operators. In particular, we will investigate spectral properties. Continuity of the spectrum and differentiability of the spectral radius of certain operators in neutron transport theory are studied as applications in the last section.