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Winter 2017 On the numerical radius of a quaternionic normal operator
Golla Ramesh
Adv. Oper. Theory 2(1): 78-86 (Winter 2017). DOI: 10.22034/aot.1611-1060

Abstract

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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Golla Ramesh. "On the numerical radius of a quaternionic normal operator." Adv. Oper. Theory 2 (1) 78 - 86, Winter 2017. https://doi.org/10.22034/aot.1611-1060

Information

Received: 22 November 2016; Accepted: 26 January 2017; Published: Winter 2017
First available in Project Euclid: 4 December 2017

zbMATH: 1367.47007
MathSciNet: MR3730356
Digital Object Identifier: 10.22034/aot.1611-1060

Subjects:
Primary: 47S10
Secondary: 35P05 , 43B15

Keywords: Compact operator , Lindenstrauss theorem , norm attaining operator , normal operator , quaternionic Hilbert space , right eigenvalue

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.2 • No. 1 • Winter 2017
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