Some results on composition operators (Q796075)

Let \(T:X\to X\) be a non-singular, measurable transformation of a \(\sigma\)-finite measure space \((X,\lambda)\). Its associated composition operator on \({\mathbb{L}}^ 2(X)\) is \(C_ T:f\to f\circ T.\) The author characterizes quasi-normal \((AA^*A=A^*AA)\) and quasi-hyponormal \((A^{*2}A^ 2\geq(A^*A)^ 2)\) composition operators in terms of the Radon-Nikodym derivatives \(d\lambda T^{-1}/d\lambda\) and \(d\lambda(T\circ T)^{-1}/d\lambda T^{-1}.\)