Some Inequalities for Selfadjoint Operators on Quaternionic Hilbert Spaces
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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.
KeywordsQuaternionic Hilbert spaces Continuous functional calculus Spectral theory Mond–Pečaric̀ method
Mathematics Subject Classification47A63 47A99
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.