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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.
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