The Spectral Theorem for Quaternionic Normal Operators

arXiv2006.05253MaRDI QIDQ6342459

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Publication date: 9 June 2020

Abstract: Let $mathcalH$ be a right quaternionic Hilbert space and let $T$ be a bounded normal right quaternionic linear operator on $mathcalH$. In this paper, we prove that there exists a unique spectral measure $E$ in $mathcalH$ such that ${\displaystyle }$T=int_{sigma_S(T)}lambda dE_lambda,${\displaystyle }$ where $sigm{a}_S(T)$ denotes the spherical spectrum of $T$.

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