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Spectral Analysis of Perturbed Fredholm Operators

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Abstract

In this proposed paper, we use a newly introduced perturbation concept in the literature originated by M. Mbekhta in J. Oper. Theo. 51, 3–18, 2004), which is the \(\Phi \)-perturbation function, allowing to derive an original stability results intervening in the theory of perturbed Fredholm operators. Our results are subsequently used to investigate a new characterization of Weyl spectrum of linear operator under such concept of \(\Phi \)-perturbation function. The last part is devoted to study the problem of the stability of perturbed semi-Fredholm operators via this kind of function approach. The theoretical results are illustrated by some examples.

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Acknowledgements

The authors would like to express their gratitude to the editor and the anonymous referees for their comments towards an improved version of the paper.

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  1. Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, BP 1171, Sfax, 3000, Tunisia

    Sana Bouzidi, Nedra Moalla & Ines Walha

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  1. Sana Bouzidi
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  2. Nedra Moalla
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  3. Ines Walha
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Correspondence to Ines Walha.

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Communicated by Fabrizio Colombo.

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Bouzidi, S., Moalla, N. & Walha, I. Spectral Analysis of Perturbed Fredholm Operators. Complex Anal. Oper. Theory 16, 87 (2022). https://doi.org/10.1007/s11785-022-01267-y

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