On power similarity of complex symmetric operators

Abstract

In this paper, we study properties of operators which are power similar to complex symmetric operators. In particular, we prove that

if $T$ is power similar to a complex symmetric operator, then $T$ is decomposable modulo a closed set $S\subset \mathbb{C}$ if and only if $R$ has the Bishop's property $(\beta)$ modulo $S$. Using the results, we get some applications of such operators.