Spectral Inclusion and Pollution for a Class of Dissipative Perturbations

Abstract

Spectral inclusion and spectral pollution results are proved for sequences of linear operators of the form $T_0 + i \gamma s_n$ on a Hilbert space, where $s_n$ is strongly convergent to the identity operator and $\gamma > 0$. We work in both an abstract setting and a more concrete Sturm-Liouville framework. The results provide rigorous justification for a method of computing eigenvalues in spectral gaps.