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The perturbation classes problem for generalized Drazin invertible operators I

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Abstract

In this paper, we are interested in the perturbation of generalized Drazin operators by compact, polynomially compact and polynomially Riesz operators. We show that the generalized Drazin spectra are invariant under commuting perturbation of these classes. We describe some relevant cases especially the case of finite spectrum.

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Acknowledgements

Funding was provided by University of Oran 1.

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Authors and Affiliations

  1. Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO), Department of Mathematics, University of Oran 1, Ahmed BEN BELLA, Oran, Algeria

    Djalel Ounadjela, Kouider Miloud Hocine & Bekkai Messirdi

Authors
  1. Djalel Ounadjela
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  2. Kouider Miloud Hocine
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  3. Bekkai Messirdi
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Correspondence to Bekkai Messirdi.

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Paper Dedicated to Professor Bekkai MESSIRDI on the occasion of his 59th Birthday.

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Ounadjela, D., Hocine, K.M. & Messirdi, B. The perturbation classes problem for generalized Drazin invertible operators I. Rend. Circ. Mat. Palermo, II. Ser 67, 159–172 (2018). https://doi.org/10.1007/s12215-017-0302-1

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  • DOI: https://doi.org/10.1007/s12215-017-0302-1

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