Weyl theorem for bounded compact perturbations (${\Sigma }_{\mathrm{e}}(L+K)={\Sigma }_{\mathrm{e}}(L)$)

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.