On perturbation of Drazin invertible linear relations

  • Y. Chamkha Sfax University, Tunisia
  • M. Kammoun Sfax University, Tunisia
Keywords: Drazin invertible linear relation, left and right Drazin invertible linear relation, perturbation of linear relations


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).


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How to Cite
Chamkha, Y., and M. Kammoun. “On Perturbation of Drazin Invertible Linear Relations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 2, Mar. 2023, pp. 269 -86, doi:10.37863/umzh.v75i2.6761.
Research articles