n-normal and n-quasinormal composition and weighted composition operators on L2(μ)

Abstract

An operator $T$ is called $n$-normal operator if$T^n{T}^{\ast }=T^{\ast }{T}^n$ and $n$-quasinormal operator if $T^n{T}^{\ast }T=T^{\ast }T{T}^n$. In this paper, the conditions under which compositionoperators and weighted composition operators become $n$-normaloperators and $n$-quasinormal operators have been obtained interms of Radon-Nikodym derivative $h_n$.