Norm estimates related to self-commutators
type: Item
instance of: scholarly article
title: Norm estimates related to self-commutators
zbMATH Open document ID: 0588.15009
DOI: 10.1016/0024-3795(86)90118-7
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: A selfadjoint matrix H with \(tr(H)=0\) can be written as a selfcommutator \(H=[T^*,T]\). The number \(\gamma (H)=\min \{\| T\|^ 2|\) \([T^*,T]=H\}\) satisfies \(\| H\| \leq \gamma (H)\leq 2\| H\|\). For the numbers \(\gamma_ n:=\sup \{\gamma (H)|\) H selfadjoint \(n\times n\)-matrix, \(tr(H)=0\), \(\| H\| \leq 1\}\) the estimates \(\gamma_{2k-1}\geq 2((k-1)/k),\) \(\gamma_{2k}\geq 2((k-1)/(k+2))\) are derived. Thus, \(\lim_{n\to \infty}\gamma_ n=2\). Finally, \(\gamma_ 5=4/3\) is shown.
Mathematics Subject Classification ID: 15A27
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 3944040
zbMATH Keywords: inequalities for the norm
zbMATH Keywords: selfadjoint
zbMATH Keywords: selfcommutator
author: Che-Kao Fong
reviewed by: G. Philip. A. Thijsse
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90118-7
OpenAlex ID: W2023048863
cites work: Which Operators are the Self-Commutators of Compact Operators?
cites work: Q5518789
Recommended article: Norms of commutators of self-adjoint operators
Recommended article: Norm Estimates for Commutators of Operators
Recommended article: Norm inequalities for commutators of self-adjoint operators
Recommended article: Estimating Norms of Commutators
Recommended article: Q4488113
Recommended article: Self-commutator norm of hyponormal Toeplitz operators
Recommended article: Q3329983
Recommended article: Estimate of the norm \(\| f(A_ 1,A_ 2)-f(B_ 1,B_ 2)\|\) for pairs of self-adjoint commuting operators
Recommended article: Q4930501
Recommended article: SPECTRAL AREA ESTIMATES FOR NORMS OF COMMUTATORS
description: scientific article; zbMATH DE number 3944040