On operators which are power similar to hyponormal operators

Abstract

In this paper, we study power similarity of operators. In particular, we show that if $T \in \mathit{PS}(H)$ (defined below) for some hyponormal operator $H$, then $T$ is subscalar. From this result, we obtain that such an operator with rich spectrum has a nontrivial invariant subspace. Moreover, we consider invariant and hyperinvariant subspaces for $T \in \mathit{PS}(H)$.