Title

Spectral theorem for quaternionic normal operators: Multiplication form

Article Type

Research Article

Publication Title

Bulletin des Sciences Mathematiques

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.

DOI

10.1016/j.bulsci.2020.102840

Publication Date

3-1-2020

Comments

Open Access, Green

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