TY  - JOUR
ID  - Otieno2005
LB  - Otieno2005
AU  - Otieno, M. O.
TI  - On intertwining and w-hyponormal operators
ST  - On intertwining and w-hyponormal operators
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2005
VL  - 25
IS  - 2
SP  - 275
EP  - 285
DO  - http://dx.doi.org/10.7494/OpMath.2005.25.2.275
UR  - http://dx.doi.org/10.7494/OpMath.2005.25.2.275
AB  - Given \(A, B\in B(H)\), the algebra of operators on a Hilbert Space \(H\), define \(\delta_{A,B}: B(H) \to B(H)\) and \(\Delta_{A,B}: B(H) \to B(H)\) by \(\delta_{A,B}(X)=AX-XB\) and \(\Delta_{A,B}(X)=AXB-X\). In this note, our task is a twofold one. We show firstly that if \(A\) and \(B^{*}\) are contractions with \(C_{.}o\) completely non unitary parts such that \(X \in \ker \Delta_{A,B}\), then \(X \in \ker \Delta_{A*,B*}\). Secondly, it is shown that if \(A\) and \(B^{*}\) are \(w\)-hyponormal operators such that \(X \in \ker \delta_{A,B}\) and \(Y \in \ker \delta_{B,A}\), where \(X\) and \(Y\) are quasi-affinities, then \(A\) and \(B\) are unitarily equivalent normal operators. A \(w\)-hyponormal operator compactly quasi-similar to an isometry is unitary is also proved.
KW  - \(w\)-hyponormal operators
KW  - contraction operators
KW  - quasi-similarity
SN  - 1232-9274
ER  -