TY  - JOUR
ID  - Pagacz2013
LB  - Pagacz2013
AU  - Pagacz, Patryk
TI  - The Putnam-Fuglede property for paranormal and ∗-paranormal operators
ST  - The Putnam-Fuglede property for paranormal and ∗-paranormal operators
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2013
VL  - 33
IS  - 3
SP  - 565
EP  - 574
DO  - http://dx.doi.org/10.7494/OpMath.2013.33.3.565
UR  - http://dx.doi.org/10.7494/OpMath.2013.33.3.565
AB  - 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.
KW  - power-bounded operators
KW  - paranormal operators
KW  - \(*\)-paranormal operators
KW  - \(k\)-paranormal operators
KW  - \(k*\)-paranormal operators
KW  - the Putnam-Fuglede theorem
SN  - 1232-9274
ER  -