(1) Prove that $S-iE$ and $S+iE$ are regular operators (2) prove that $U=i(S+iE)^{-1} (S-iE)$ is unitary operator and that none of its eigenvalues is $1$
Ok so first part is fairly easy. As for the 2. part I proved that U is unitary operator, however I'm having trouble proving that none of its eigenvalues are $1.$ I suppose I should suppose the opposite and stumble upon a contradiction of some sort?