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The bilateral shift $(Tx{)}_n=x_{n+1}$ is unitary. It has empty point spectrum, while its approximate point spectrum is the unit circle. For $|\lambda |=1$, normalized vectors with entries ${\lambda }^n$ on an interval of length $N$ fail to satisfy $Tx=\lambda x$ only at the two endpoints, giving residual norm $\sqrt{2/N}$.

It is the two-sided sequence case of a shift operator.