@Article{Pagacz2013,
author = "Pagacz, Patryk",
title = "The Putnam-Fuglede property for paranormal and ∗-paranormal operators",
journal = "Opuscula Math.",
year = "2013",
volume = "33",
number = "3",
pages = "565--574",
doi = "http://dx.doi.org/10.7494/OpMath.2013.33.3.565",
url = "http://dx.doi.org/10.7494/OpMath.2013.33.3.565",
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",
issn = "1232-9274"
}