Separating partial normality classes with composition operators. (English) Zbl 1114.47027

The authors obtain complete measure-theoretic characterizations of \(\infty\)-hyponormal, \(p\)-hyponormal and weakly-hyponormal composition operators (i.e., \(w\)-hyponormal). Then they obtain that if a composition operator is \(w\)-hyponormal, then it has an nontrivial invariant subspace.
Next, the authors give concrete examples of \(p\)-hyponormal, \(\infty\)-hyponormal, quasinormal, weakly-hyponormal and subnormal composition operators.


47B33 Linear composition operators
47B20 Subnormal operators, hyponormal operators, etc.