Some relationships with subnormal operators and existence of hyperinvariant subspaces

Maria F. Gamal'

If $T$ is a polynomially bounded operator, $\mathcal{M}$ is an invariant subspace of $T$, $T{|}_{\mathcal{M}}$ is a unilateral shift and $T^{\ast }{|}_{{\mathcal{M}}^{\perp }}$ is subnormal, then $T…