Opuscula Mathematica

Opuscula Math.
, no. 2
 (), 275-285
Opuscula Mathematica

On intertwining and w-hyponormal operators

Abstract. 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.
Keywords: \(w\)-hyponormal operators, contraction operators, quasi-similarity.
Mathematics Subject Classification: 47B20.
Cite this article as:
M. O. Otieno, On intertwining and w-hyponormal operators, Opuscula Math. 25, no. 2 (2005), 275-285
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

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.