Opuscula Math. 33, no. 3 (2013), 565-574

Opuscula Mathematica

The Putnam-Fuglede property for paranormal and ∗-paranormal operators

Patryk Pagacz

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.

Full text (pdf)

  • 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.
Opuscula Mathematica - cover

Cite this article as:
Patryk Pagacz, The Putnam-Fuglede property for paranormal and ∗-paranormal operators, Opuscula Math. 33, no. 3 (2013), 565-574, http://dx.doi.org/10.7494/OpMath.2013.33.3.565

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.