Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 1361–1375 | Cite as

The Perturbation Classes Problem for Generalized Drazin Invertible Operators II

  • Djalel Ounadjela
  • Mohammed BenharratEmail author
  • Bekkai Messirdi


We investigate the perturbation problems of left and right generalized Drazin invertibility of bounded linear operators on Hilbert spaces. Some algebraic and topological characterizations are presented and some new perturbation results are obtained essentially via the quasinilpotent part and the analytic core. We also investigate some relationships between these interior points and other operators related to Fredholm theory, particularly left Browder operators as well as right Browder operators.


Generalized Drazin invertible operators Left and right generalized Drazin invertible operators Perturbation Quasinilpotent part Analytic core Left and right Browder operators 

Mathematics Subject Classification

Primary 47A10 47A55 Secondary 47B06 47B07 



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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Exact and Applicable SciencesUniversity of Oran 1OranAlgeria
  2. 2.Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO)OranAlgeria
  3. 3.Department of Mathematics and InformaticsNational Polytechnic School of Oran - Maurice Audin (ex. ENSET d’Oran.)OranAlgeria
  4. 4.High School of Electrical and Energy EngineeringESG2E OranOranAlgeria

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