Perturbation results for linear operators and applications to the transport equation

International audienceWe prove that the components of the freholm domains for closed linear operators on Banach spaces remain invariant under additive perturbations belonging to broad classes of perturbing operators. Although our approach is somewhat different than the standard one used to discuss the stability of essencial spectra of such operators, our results provide a natural extension of many known ones in the litterature and, in particular, of those obtained in the woks [18,19