= Translation of the spectrum by a scalar
{title2=$\sigma(x+\alpha e)=\alpha+\sigma(x)$}
The identity $(x+\alpha e)-\lambda e=x-(\lambda-\alpha)e$ proves the formula directly from invertibility. In a nonzero complex unital <Banach algebra>, the <nonemptiness of the Banach-algebra spectrum> implies that if $x$ is a <quasinilpotent element>, then $\rho(x+e)=1$. Consequently every nonscalar element cannot simultaneously be quasinilpotent: adding the identity preserves nonscalarity while translating its spectrum.
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