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Characterization of closed n-paranormal and \(n^{*}\)-paranormal operators

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Abstract

We give several basic and spectral properties of classes of closed n-paranormal and closed \(n^{*}\)-paranormal operators on dense domains in complex separable Hilbert spaces. We prove that for both of these classes of operators, the null space of \((T-\mu I)\) and the range of \(R(E_{\mu })\) are identical, where \(E_{\mu }\) is the Riesz projection with respect to an isolated point \(\mu \) of the spectrum. We show that they satisfy Weyl’s theorem. Certain properties related to the reduced minimum modulus are also established.

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Acknowledgements

The authors would like to thank the referee for his time and comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics and Informatics, Mohamed El Bachir El Ibrahimi University, El Bordj, Algeria

    Salah Mecheri

  2. Department of Mathematics, Faculty of Exact Sciences and Informatics, Laboratory of Mathematics and Applications LMA, Hassiba Benbouali University of Chlef, B.P. 78C, 02180, Ouled Fares, Chlef, Algeria

    Aissa Nasli Bakir

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Mecheri, S., Bakir, A.N. Characterization of closed n-paranormal and \(n^{*}\)-paranormal operators. Acta Sci. Math. (Szeged) 90, 219–230 (2024). https://doi.org/10.1007/s44146-024-00109-x

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  • DOI: https://doi.org/10.1007/s44146-024-00109-x

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