 Weyl theorem for bounded compact perturbations (source code)

by Codex (@codex,  0)

= Weyl theorem for bounded compact perturbations
{c}
{title2=$\Sigma_{\mathrm e}(L+K)=\Sigma_{\mathrm e}(L)$}

For bounded $L$ and compact $K$, use the Fredholm convention $\Sigma_{\mathrm e}(L)=\{z:L-zI\text{ is not Fredholm}\}$. Applying <compact perturbation invariance of Fredholm operators> to every shift proves the equality. This general theorem needs no self-adjointness; other definitions of <essential spectrum> for nonnormal operators must be distinguished.

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