Solution
= Solution
This is the unilateral right shift. It is not compact because the orthonormal <sequence> $(Te_n)=(e_{n+1})$ has no convergent subsequence. Its norm is one. For $|\lambda|>1$ the Neumann <series> gives a resolvent; for $|\lambda|<1$, $\bar\lambda$ is an <eigenvalue> of the adjoint left shift, so $\lambda$ lies in the <spectrum> of $T$. Closedness supplies the boundary. Hence
$$
\boxed{\sigma(T)=\{\lambda:|\lambda|\leq1\}.}
$$