@article{Chamkha_Kammoun_2023, title={On perturbation of Drazin invertible linear relations}, volume={75}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6761}, DOI={10.37863/umzh.v75i2.6761}, abstractNote={<p>UDC 517.98</p> <p>We study the stability of regular, finite ascent, and finite descent linear relations defined in Banach spaces under commuting nilpotent operator perturbations.<span class="Apple-converted-space"> </span>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.<span class="Apple-converted-space"> </span>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).</p>}, number={2}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Chamkha, Y. and Kammoun, M.}, year={2023}, month={Mar.}, pages={269 - 286} }