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Riesz Projection and Essential S-spectrum in Quaternionic Setting

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Abstract

This paper is devoted to the investigation of the Weyl and the essential S-spectra of a bounded right quaternionic linear operator in a right quaternionic Hilbert space. Using the quaternionic Riesz projection, the S-eigenvalue of finite type is both introduced and studied. In particular, we have shown that the Weyl and the essential S-spectra do not contain eigenvalues of finite type. We have also described the boundary of the Weyl S-spectrum and the particular case of the spectral theorem of the essential S-spectrum.

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Acknowledgements

We would like to thank the reviewers for taking the time and effort necessary to review the manuscript. We sincerely appreciate all valuable comments and suggestions, which helped us to improve the quality of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Gafsa, University of Gafsa, 2112, Zarroug, Tunisia

    Hatem Baloudi

  2. Departement of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Route de Soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisia

    Sayda Belgacem & Aref Jeribi

Authors
  1. Hatem Baloudi
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  2. Sayda Belgacem
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  3. Aref Jeribi
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Correspondence to Hatem Baloudi.

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Communicated by Fabrizio Colombo.

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This article is part of the topical collection “Spectral Theory and Operators in Mathematical Physics” edited by Jussi Behrndt and Fabrizio Colombo.

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Baloudi, H., Belgacem, S. & Jeribi, A. Riesz Projection and Essential S-spectrum in Quaternionic Setting. Complex Anal. Oper. Theory 16, 95 (2022). https://doi.org/10.1007/s11785-022-01276-x

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