Let $H$ be a complex [Hilbert space](/page/Hilbert%20Space) and let $T\in\mathcal{L}(H)$ be normal. If $\lambda\in\sigma(T)$, then $\lambda$ is an approximate eigenvalue of $T$; equivalently, there exists a sequence $(h_n)_{n=1}^{\infty}$ in $H$ such that