## 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.

### MSC:

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