 Finite-section approximation of a compact operator (source code)

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= Finite-section approximation of a compact operator

If finite-rank orthogonal projections $P_n$ converge strongly to the identity and $A$ is compact, then $\lVert A-P_nAP_n\rVert\to0$. The finite-section spectra converge to $\operatorname{Sp}(A)$ in Hausdorff distance, including for nonnormal $A$.

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