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.

DOI: 10.14232/actasm-018-582-z

AMS Subject Classification (1991): 47A15; 47A60, 47A10

Keyword(s): hyperinvariant subspace, polynomially bounded operator

Received September 12, 2018 and in final form April 4, 2019. (Registered under 82/2018.)