A multiplicative property characterizes quasinormal composition operators in $L^2$-spaces

Abstract

A densely defined composition operator in an $L^2$-space induced by a measurable transformation $\varphi$ is shown to be quasinormal if and only if the Radon-Nikodym derivatives $h_{{\varphi }^n}$ attached to powers ${\varphi }^n$ of $\varphi$ have the multiplicative property: $h_{{\varphi }^n}=h_{\varphi }^n$ almost everywhere for n = 0, 1, 2, ....

8 pages