Singular value inequalities for compact operators
type: Item
instance of: scholarly article
title: Singular value inequalities for compact operators
zbMATH Open document ID: 1263.47018
author: Wasim Audeh
author: Fuad Kittaneh
published in: Linear Algebra and its Applications
publication date: 2012-11-09T00:00:00Z
review text: In [SIAM J. Matrix Anal. Appl. 11, No. 2, 272--277 (1990; Zbl 0704.47014)], \textit{R. Bhatia} and \textit{F. Kittaneh} established the arithmetic-geometric mean inequality for compact operators \(A,B\) on a separable Hilbert space as \[ 2S_j(AB^*)\leq S_j(A^*A+B^*B). \] Some inequalities equivalent to this one can be found in the literature. In the paper under review, the authors prove another equivalent inequality, namely, \[ 2s_j(A)\leq S_j((B+A)\oplus(B-A)), \] where \(A\) is selfadjoint operator, \(B\geq0\) and \(\pm A\leq B\). As an application, they are able to prove a Cauchy-Schwarz type inequality and a triangle-type inequality.
reviewed by: Maryam Khosravi
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 6104554
zbMATH Keywords: singular value
zbMATH Keywords: compact operator
zbMATH Keywords: inequality
zbMATH Keywords: positive operator
zbMATH Keywords: self-adjoint operator
zbMATH Keywords: arithmetic-geometric mean
MaRDI profile type: Publication
full work available at URL: j.laa.2012.06.032
OpenAlex ID: W2027687268
cites work: On the Singular Values of a Product of Operators
cites work: The matrix arithmetic-geometric mean inequality revisited
cites work: Interpolation zwischen den Klassen 𝔖p von Operatoren in Hilberträumen
cites work: Inequalities for sums and direct sums of Hilbert space operators
cites work: Some Norm Inequalities for Operators
cites work: More results on singular value inequalities of matrices
cites work: Singular values of differences of positive semidefinite matrices
DOI: 10.1016/J.LAA.2012.06.032
description: scientific article; zbMATH DE number 6104554