Spectral theorem for quaternionic compact normal operators

Ramesh, G and Santhosh Kumar, P (2017) Spectral theorem for quaternionic compact normal operators. The Journal of Analysis, 25 (1). pp. 65-81. ISSN 0971-3611

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In this article, we prove two versions of the spectral theorem for quaternionic compact normal operators, namely the series representation and the resolution of identity form. Though the series representation form already appeared in [5], we prove this by using simultaneous diagonalization. Whereas the resolution of identity is new in the literature for the quaternion case, we prove this by associating a complex linear operator to the given right linear operator and applying the classical result. In this process we prove some spectral properties of compact operators parallel to the classical theory. We also establish the singular value decomposition of a compact operator.

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IITH Creators:
IITH CreatorsORCiD
Item Type: Article
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 28 May 2019 11:04
Last Modified: 28 May 2019 11:04
URI: http://raiith.iith.ac.in/id/eprint/5359
Publisher URL: http://doi.org/10.1007/s41478-017-0027-8
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