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 is an element of 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 is an element of PS(H).