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Let $\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be abounded normal right quaternionic linear operator on $\mathcal{H}$. In thispaper, 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 $T$.

The Spectral Theorem for Quaternionic Normal Operators