Special classes of positive and completely positive maps
type: Item
instance of: scholarly article
title: Special classes of positive and completely positive maps
zbMATH Open document ID: 0874.15002
DOI: 10.1016/S0024-3795(96)00776-8
author: Chi-Kwong Li
author: Hugo J. Woerdeman
published in: Linear Algebra and its Applications
publication date: 1997-11-03T00:00:00Z
review text: Many authors have studied the problem of characterising the positive and completely positive maps on square complex matrices of size \(n\) under certain invariant conditions. These authors have characterized the above mentioned maps that leave invariant the diagonal or the \(k\)th elementary symmetric functions of the diagonal entries, for \(1 < k \leq n.\) The case \(k=1\) corresponding to the trace function has already been studied by different authors. Here the authors also show that such a positive map is always decomposable if \(n \leq 3\) but fails for \(n > 3.\) The results for the real case are deduced from the complex case which requires minor modifications.
reviewed by: Arbind Kumar Lal
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 999974
zbMATH Keywords: completely positive maps
zbMATH Keywords: symmetric functions
zbMATH Keywords: correlation matrix
zbMATH Keywords: decomposibility of positive linear maps
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 999974