On perturbation of Drazin invertible linear relations

Abstract

UDC 517.98 We study the stability of regular, finite ascent, and finite descent linear relations defined in Banach spaces under commuting nilpotent operator perturbations. As an application, we give the invariance theorem of Drazin invertible spectrum under these perturbations. We also focus on the study of some properties of the left and right Drazin invertible linear relations. It is proved that, for bounded and closed left (resp., right) Drazin invertible linear relation with nonempty resolvent set, 0 is an isolated point of the associated approximate point spectrum (resp., surjective spectrum).