Cones and norms in the tensor product of matrix spaces.
type: Item
instance of: scholarly article
title: Cones and norms in the tensor product of matrix spaces.
zbMATH Open document ID: 1041.15021
author: D. Massart
published in: Linear Algebra and its Applications
publication date: 2004-03-14T00:00:00Z
review text: In the tensor product \({\mathbb M}_{n,m}\) of two matrix spaces \({\mathbb M}_m\) and \({\mathbb M}_n\) three natural cones are considered. The first one \({\mathcal P}_0\) consists of positive semi-definite matrices; the second one \({\mathcal P_+}\) is generated by tensor products of positive semi-definite matrices in the factor spaces; \({\mathcal P_-}\) is defined as the dual cone for~\({\mathcal P}_+\). In~\({\mathbb M}_{n,m}\) several tensor norms generated by spectral and/or trace norms in the factor space are considered. The author studies relationships among these norms as well as relations among the three kinds of order intervals in the tensor product.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 2056675
zbMATH Keywords: cones of matrices
zbMATH Keywords: norms of matrices
zbMATH Keywords: tensor product of matrix spaces
zbMATH Keywords: spectral norm
zbMATH Keywords: trace norm
zbMATH Keywords: majorants
zbMATH Keywords: estimates of norms
reviewed by: A. R. Alimov
MaRDI profile type: Publication
full work available at URL: j.laa.2003.06.005
OpenAlex ID: W2094503062
cites work: Q5601153
cites work: Q5690490
cites work: Completely positive linear maps on complex matrices
cites work: Spectral bounds derived from quadratic forms on decomposable tensors
cites work: The Grothendieck inequality for bilinear forms on \(C^*\)-algebras
cites work: Q4879849
cites work: Q4080169
cites work: Q4722624
cites work: Theory of operator algebras I.
cites work: Q4435456
DOI: 10.1016/J.LAA.2003.06.005
description: scientific article; zbMATH DE number 2056675