Abstract
In a right quaternionic Hilbert space, for a bounded right linear operator, the Kato S-spectrum is introduced and studied to a certain extent. In particular, it is shown that the Kato S-spectrum is a non-empty compact subset of the S-spectrum and it contains the boundary of the S-spectrum. Using right-slice regular functions, local S-spectrum, at a point of a right quaternionic Hilbert space, and the local spectral subsets are introduced and studied. The S-surjectivity spectrum and its connections to the Kato S-spectrum, approximate S-point spectrum and local S-spectrum are investigated. The generalized Kato S-spectrum is introduced and it is shown that the generalized Kato S-spectrum is a compact subset of the S-spectrum.
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Acknowledgements
K. Thirulogasanthar would like to thank the FRQNT, Fonds de la Recherche Nature et Technologies (Quebec, Canada) for partial financial support under the Grant number 2017-CO-201915. Part of this work was done while he was visiting the University of Jaffna to which he expresses his thanks for the hospitality.
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Communicated by Uwe Kähler.
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Thirulogasanthar, K., Muraleetharan, B. Kato S-Spectrum in the Quaternionic Setting. Adv. Appl. Clifford Algebras 30, 40 (2020). https://doi.org/10.1007/s00006-020-01064-w
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DOI: https://doi.org/10.1007/s00006-020-01064-w
Keywords
- Quaternions
- Quaternionic Hilbert spaces
- S-spectrum
- Semi-regular operator
- Approximate S-point spectrum
- Surjectivity S-spectrum
- Kato S-spectrum