Indecomposable positive maps in low dimensional matrix algebras
type: Item
instance of: scholarly article
title: Indecomposable positive maps in low dimensional matrix algebras
zbMATH Open document ID: 0733.15007
DOI: 10.1016/0024-3795(91)90211-E
author: N. E. Zubov
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: Consider a linear map from the n by n matrix algebra \(M_ n({\mathbb{C}})\) into itself. The map is said to be positive if it sends the subset of positive semidefinite matrices into itself. This paper continues the work of \textit{M. D. Choi} [Proc. Symp. Pure Math. 38, Part 2, Kingston/Ont. 1980, 583-590 (1982; Zbl 0522.46037)] and of \textit{K. Tanahashi} and \textit{J. Tomiyama} [Can. Math. Bull. 31, No.3, 308- 317 (1988; Zbl 0679.46044)] on the question of decomposing positive linear maps into a sum of completely positive and completely copositive components. In particular, the author analyzes the degree of indecomposability of certain positive linear maps on \(M_ n({\mathbb{C}})\) for \(n=4,5\).
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 4212237
zbMATH Keywords: indecomposable positive
zbMATH Keywords: low-dimensional matrix algebras
zbMATH Keywords: positive semidefinite matrices
zbMATH Keywords: positive linear maps
zbMATH Keywords: degree of indecomposability
reviewed by: Thomas A. Farmer
MaRDI profile type: Publication
cites work: Positive semidefinite biquadratic forms
cites work: Q4748635
cites work: Q3672499
cites work: Schwarz inequalities and the decomposition of positive maps on C*-algebras
cites work: Positive Projections on C∗ -Algebras and an Extremal Positive Map
cites work: Positive linear maps of operator algebras
cites work: On positive linear maps between matrix algebras
cites work: Indecomposable Positive Maps in Matrix Algebras
cites work: Positive maps of low dimensional matrix algebras
description: scientific article; zbMATH DE number 4212237