Spectral theorem for quaternionic normal operators: Multiplication form

G, Ramesh and Santhosh Kumar, P (2020) Spectral theorem for quaternionic normal operators: Multiplication form. Bulletin des Sciences Mathematiques, 159. ISSN 0007-4497

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Abstract

Let H be a right quaternionic Hilbert space and let T be a quaternionic normal operator with domain D(T)⊂H. We prove that there exists a Hilbert basis N of H, a measure space (Ω0,ν), a unitary operator U:H→L2(Ω0;H;ν) and a ν-measurable function η:Ω0→C such that Tx=U⁎MηUx,for allx∈D(T) where Mη is the multiplication operator on L2(Ω0;H;ν) induced by η with U(D(T))⊆D(Mη). We show that every complex Hilbert space can be seen as a slice Hilbert space of some quaternionic Hilbert space and establish the main result by reducing the problem to the complex case then lift it to the quaternion case.

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IITH Creators:

IITH Creators	ORCiD
G, Ramesh	UNSPECIFIED

Item Type:

Article

Uncontrolled Keywords:

Functional calculus, Quaternionic Hilbert space, Quaternionic normal operator, Slice complex plane,Spectral measure,Spectral theorem, Indexed in Scopus

Subjects:

Mathematics

Divisions:

Department of Mathematics

Depositing User:

Team Library

Date Deposited:

27 Feb 2020 05:54

Last Modified:

27 Feb 2020 05:54

URI:

http://raiithold.iith.ac.in/id/eprint/7477