Opuscula Math. 33, no. 3 (2013), 565-574
http://dx.doi.org/10.7494/OpMath.2013.33.3.565
Opuscula Mathematica
The Putnam-Fuglede property for paranormal and ∗-paranormal operators
Abstract. An operator \(T \in {\cal B}(H)\) is said to have the Putnam-Fuglede commutativity property (PF property for short) if \(T^*X = XJ\) for any \(X \in {\cal B}(K,H)\) and any isometry \(J \in {\cal B}(K)\) such that \(TX = XJ^*\). The main purpose of this paper is to examine if paranormal operators have the PF property. We prove that \(k*\)-paranormal operators have the PF property. Furthermore, we give an example of a paranormal without the PF property.
Keywords: power-bounded operators, paranormal operators, \(*\)-paranormal operators, \(k\)-paranormal operators, \(k*\)-paranormal operators, the Putnam-Fuglede theorem.
Mathematics Subject Classification: 47B20, 47A05, 47A62.
- Patryk Pagacz
- Uniwersytet Jagielloński, Instytut Matematyki, ul. Łojasiewicza 6, PL-30348 Kraków, Poland
- Received: 2012-06-20.
- Revised: 2013-01-23.
- Accepted: 2013-02-12.
