## Paranormal contractions have property PF.(English)Zbl 1084.47006

In the paper, several important notions of operator classes as well as the relationship among these classes are introduced first. Then the authors provide a new proof for the assertion that the Putnam-Fuglede commutativity property holds for paranormal contractions. In addition, they extend their results, and show that the Putnam-Fuglede commutativity property still holds for $$k$$-quasihyponormal contractions and $$p$$-paranormal contractions.

### MSC:

 47A45 Canonical models for contractions and nonselfadjoint linear operators 47B20 Subnormal operators, hyponormal operators, etc.