Approximate eigenvalue
= Approximate eigenvalue
{title2=$\lambda\in\sigma_{\mathrm{ap}}(T)$}
An approximate eigenvalue of a bounded operator $T$ is a scalar $\lambda$ admitting unit vectors $x_n$ with $\|(T-\lambda I)x_n\|\to0$. Every approximate eigenvalue belongs to the <spectrum>; for a <normal operator>, all spectral points are approximate eigenvalues.