 Orthogonal eigenvectors of a compact operator (source code)

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= Orthogonal eigenvectors of a compact operator

If $Tx_j=\lambda_jx_j$ for an infinite orthonormal sequence $(x_j)$ and a compact operator $T$ on a <Hilbert space>, then $\lambda_j\to0$. Otherwise a subsequence of the vectors $Tx_j$ stays pairwise separated, contradicting compactness.

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