Class \(wA(s,t)\) operators and quasisimilarity
type: Item
instance of: scholarly article
title: Class \(wA(s,t)\) operators and quasisimilarity
zbMATH Open document ID: 1276.47028
DOI: 10.4171/PM/1919
published in: Portugaliae Mathematica. Nova Série
publication date: 2013-03-12T00:00:00Z
review text: The paper under review is partly motivated by the Fuglede-Putnam theorem, which can be rephrased as follows. For operators \(S, T \in B(\mathcal H),\) consider the operator \(\delta_{T, S}\) on \(B(\mathcal H)\) given by \[ \delta_{T, S}(X)=TX-XS. \] If \(S, T\) are normal operators, then \(\ker (\delta_{T, S})=\ker(\delta_{T^*, S^*}).\) A number of generalizations of this result to various classes (including subnormal and hyponormal operators) can be found in the literature. For instance, the inclusion \(\ker (\delta_{T, S}) \subseteq \ker(\delta_{T^*, S^*})\) can be ensured under hypotheses weaker than normality of \(S\) and \(T.\) Although it is difficult to reproduce the definition of the class of \(wA(s, t)\) operators, we note that this class contains the class of the so-called \(w\)-hyponormal operators. It is unfortunate that the paper does not contain a single concrete example of operators belonging to the class \(wA(s, t)\), other than known examples. Some results related to quasi-similar class \(wA(s, t)\) operators are also discussed.
reviewed by: Sameer Chavan
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A11
zbMATH DE Number: 6143506
zbMATH Keywords: class \(wA(s
zbMATH Keywords: t)\) operators
zbMATH Keywords: Fuglede-Putnam theorem
zbMATH Keywords: quasisimilarity
author: Mohammad H. M. Rashid
MaRDI profile type: Publication
cites work: On p-hyponormal operators for \(0<p<1\)
cites work: An Operator Inequality Which Implies Paranormality
cites work: \(w\)-hyponormal operators
cites work: Properties which normal operators share with normal derivations and related operators
cites work: Q5655951
cites work: Fuglede-Putnam's theorem for w-hyponormal operators
cites work: Extensions of a Theorem of Fuglede and Putnam
cites work: Putnam's Inequality for p-Hyponormal Operators
cites work: An operator transform from class A to the class of hyponormal operators and its application
cites work: On quasisimilarity for subnormal operators
cites work: Q3999065
cites work: On generalised Putnam-Fuglede theorems
cites work: Quasi-similar \(p\)-hyponormal operators
cites work: A remark on generalised Putnam-Fuglede theorems
cites work: Classes of operators determined by the Heinz-Kato-Furuta inequality and the Hölder-McCarthy inequality
cites work: Q4506071
cites work: On the class of paranormal operators
cites work: Q4257793
cites work: Q3961338
cites work: Q4700365
cites work: \(p\)-hyponormal operators and quasisimilarity
cites work: On p-quasihyponormal operators and quasisimilarity
cites work: ON QUASISIMILARITY FOR LOG-HYPONORMAL OPERATORS
cites work: Aluthge transforms of operators
cites work: The Fuglede--Putnam theorem for \((p,k)\)-quasihyponormal operators
cites work: Normal Derivations in Norm Ideals
cites work: ON A CLASS OF OPERATORS RELATED TO PARANORMAL OPERATORS
cites work: Q5756301
cites work: Quasinormality and Fuglede--Putnam theorem for class \(A(s,t)\) operators
cites work: An extension of Putnam-Fuglede theorem for hyponormal operators
cites work: Q3559458
cites work: On the spectra of some non-normal operators
cites work: Weyl type theorems and class A(s,t) operators
cites work: On Hyponormal Operators
cites work: Q4090924
cites work: Q3925415
cites work: Q3023562
cites work: Operators Similar to Their Adjoints
cites work: Q3933486
cites work: Relations between two inequalities \((B^{\frac r2} A^p B^{\frac r2})^{\frac r{p+r}}\geq B^r\) and \(A^p\geq(A^{\frac p2} B^r A^{\frac p2})^{\frac p{p+r}}\) and their applications
description: scientific article; zbMATH DE number 6143506