On Structured Perturbations of Positive Semigroups

In this note we generalize perturbation results for positive $C_0$-semigroups on AM- and AL-spaces and give a Weiss–Staffans type perturbation result for generators of positive semigroups on Banach lattices. The abstract results are applied to domain perturbations of generators, a heat equation with boundary feedback and perturbations of the first derivative.