The commuting graph of bounded linear operators on a Hilbert space
type: Item
instance of: scholarly article
title: The commuting graph of bounded linear operators on a Hilbert space
zbMATH Open document ID: 1272.47045
author: Janko Bračič
author: Călin-Grigore Ambrozie
author: Bojan Kuzma
author: Vladimír Müller
published in: Journal of Functional Analysis
publication date: 2013-03-04T00:00:00Z
review text: The authors of the paper under review prove that there exists an operator \(T\) on a separable infinite-dimensional Hilbert space such that the commutant of every operator which is not a scalar multiple of the identity operator and commutes with \(T\) coincides with the commutant of \(T\). Furthermore, they study finite-rank operators, normal operators, partial isometries, \(\mathcal C_{0}\)-contractions, and show that for these classes of operators it is possible to construct a finite sequence of operators, starting with a given operator and ending with a rank-one projection, such that each operator in the sequence commutes with its predecessor. At the end, they prove that, for any given set of \textit{yes/no} conditions between points in some finite set, there always exist operators on a finite-dimensional Hilbert space such that their commutativity relations exactly satisfy those conditions.
reviewed by: Ajda Fošner
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 6140893
zbMATH Keywords: Hilbert space operators
zbMATH Keywords: commutativity
zbMATH Keywords: commuting graph
MaRDI profile type: Publication
full work available at URL: j.jfa.2012.11.011
OpenAlex ID: W1972572248
DOI: 10.1016/J.JFA.2012.11.011
description: scientific article; zbMATH DE number 6140893