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

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

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