Recall that \(A \in \mathcal {B}(\mathcal {H})\) is normalNormal operator if \(A^{*}A = A A^{*}\) . This class of operators is perhaps the most understood class of bounded Hilbert space operators since the spectral theorem says that every normal operator can be represented, via unitary equivalence, as a multiplication operator \(f \mapsto \phi f\) on a Lebesgue space \(L^2(\mu , X)\) for some compact Hausdorff space X, some positive finite Borel measure \(\mu \) on X, and some \(\phi \in L^{\infty }(\mu , X)\) . Various refinements of the spectral theorem give us further information about a generic normal operator.