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arXiv · 2006.05253

The Spectral Theorem for Quaternionic Normal Operators

El Hassan Benabdi·Mohamed Barraa
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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 $$T=\int_{\sigma_S(T)}\lambda dE_\lambda,$$ where $\sigma_S(T)$ denotes the spherical spectrum of $T$.

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El Hassan Benabdi, Mohamed Barraa. 2020-06-09. The Spectral Theorem for Quaternionic Normal Operators. https://arxiv.org/abs/2006.05253

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