We study the problem of stability of regular, finite ascent, and finite descent linear relations defined in Banach spaces under commuting nilpotent operator perturbations. As an application, we present the invariance theorem for the 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 a 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).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 2, pp. 269–286, February, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i2.6761.
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Chamkha, Y., Kammoun, M. On Perturbation of Drazin Invertible Linear Relations. Ukr Math J 75, 305–327 (2023). https://doi.org/10.1007/s11253-023-02200-y
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DOI: https://doi.org/10.1007/s11253-023-02200-y