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Some Inequalities for Selfadjoint Operators on Quaternionic Hilbert Spaces

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Abstract

In this paper, we prove some inequalities between quaternionic bounded selfadjoint operators on quaternionic Hilbert spaces. We follow the Mond–Pečaric̀ method in operator inequalities in case of complex Hilbert spaces and obtain the similar inequalities in the quaternionic setting. The results are applied to prove some inequalities for positive quaternionic operators.

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Acknowledgements

The authors appreciate the AE and the referees for their valuable comments which improved the presentation of the paper. Also, the authors would like to thank Professor M. Sal Moslehian from Ferdowsi University of Mashhad for providing some of the main references.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, 91775, Iran

    S. Mahdipour, A. Niknam & M. Fashandi

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  1. S. Mahdipour
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  2. A. Niknam
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  3. M. Fashandi
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Correspondence to M. Fashandi.

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Communicated by Eckhard Hitzer

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Mahdipour, S., Niknam, A. & Fashandi, M. Some Inequalities for Selfadjoint Operators on Quaternionic Hilbert Spaces. Adv. Appl. Clifford Algebras 30, 5 (2020). https://doi.org/10.1007/s00006-019-1032-6

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  • DOI: https://doi.org/10.1007/s00006-019-1032-6

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