The Spectral Theorem for Quaternionic Normal Operators

Abstract

Let $\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be a bounded normal right quaternionic linear operator on $\mathcal{H}$. In this paper, we prove that there exists a unique spectral measure $E$ in $\mathcal{H}$ such that $$T={\int }_{{\sigma }_S(T)}\lambda d{E}_{\lambda },$$ where ${\sigma }_S(T)$ denotes the spherical spectrum of $T$.

References in corpus (1)

• A new approach to the S-functional calculus