On the numerical radius of a quaternionic normal operator

G, Ramesh (2017) On the numerical radius of a quaternionic normal operator. Advances in Operator Theory, 2 (1). pp. 78-86. ISSN 2538-225X

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We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known fact that a non zero quaternionic compact normal operator has a non zero right eigenvalue. Using this we give a new proof of the spectral theorem for quaternionic compact normal operators. Finally, we show that every quaternionic compact operator is norm attaining and prove the Lindenstrauss theorem on norm attaining operators, namely, the set of all norm attaining quaternionic operators is norm dense in the space of all bounded quaternionic operators defined between two quaternionic Hilbert spaces.

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IITH Creators:
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Item Type: Article
Uncontrolled Keywords: quaternionic Hilbert space, normal operator, compact operator, right eigenvalue, norm attaining operator, Lindenstrauss theorem
Subjects: Mathematics
Mathematics > Numerical analysis
Divisions: Department of Mathematics
Depositing User: Library Staff
Date Deposited: 15 Nov 2017 11:50
Last Modified: 16 Nov 2017 03:57
URI: http://raiith.iith.ac.in/id/eprint/3666
Publisher URL: https://doi.org/10.22034/aot.1611-1060
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