= Two-endpoint symmetric derivative has whole complex spectrum
{title2=$A_0f=if',\quad D(A_0)=H_0^1(0,1),\quad\sigma(A_0)=\mathbb C$}
Its adjoint is $if'$ on all of $H^1(0,1)$, with no endpoint conditions. Every complex $\lambda$ is an adjoint eigenvalue, with eigenfunction $e^{-i\lambda x}$. Thus every complex $\lambda$ obstructs surjectivity of $\lambda I-A_0$. The original operator has no eigenvalues because its zero initial value kills any solution of $if'=\lambda f$.
// Target: analysis.bigb
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