Invertibility of functions of operators and existence of hyperinvariant subspaces

Abstract

Let $T$ be an absolutely continuous polynomially bounded operator, and let $\theta$ be a singular inner function. It is shown that if $\theta (T)$ is invertible and some additional conditions are fulfilled, then $T$ has nontrivial hyperinvariant subspaces.

Many inaccuracies and misprints are corrected by the referee