Fuglede-Putnam Theorem and Quasi-nilpotent part of n-power normal operators

Abstract

In this article we show that the following properties hold for $n$-power normal operators $T$:(i) $T$ has the Bishop's property$(\beta)$.(ii) $T$ is isoloid.(iii) $T$ is invariant under tensor product.(iv) $T$ satisfies the Fuglede-Putnam theorem.(v) $T$ is of finite ascent and descent.(vi) The Quasi-nilpotent part of $T$ reduces $T$.