Extremal matrix states on tensor product of \(C^{*}\)-algebras
type: Item
instance of: scholarly article
title: Extremal matrix states on tensor product of \(C^{*}\)-algebras
zbMATH Open document ID: 1305.46051
author: Wei Wu
published in: Monatshefte für Mathematik
publication date: 2014-08-15T00:00:00Z
review text: A matrix state on a unital \(C^\ast\)-algebra \(A\) is a unital, completely positive, linear map \(A\to \mathbb M_n\) where \(n\in\mathbb N\). The matrix state space \(\mathcal{CS}(A)\) is the set of all matrix states on \(A\). It can be expressed as \(\bigcup_{n}K_n\) where \(K_n\subseteq M_n(A^\ast)\) and it is matrix convex. The present paper describes the matrix extremal points of \(\mathcal{CS}(A)\) when \(A\) is the tensor product of two unital \(C^\ast\)-algebras and at least one of them is of type I.
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 47L25
zbMATH DE Number: 6330898
zbMATH Keywords: matrix convexity
zbMATH Keywords: matrix state space
zbMATH Keywords: matrix extreme point
reviewed by: Emmanuel Chetcuti
MaRDI profile type: Publication
full work available at URL: s00605-014-0632-4
OpenAlex ID: W2018833859
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DOI: 10.1007/S00605-014-0632-4
description: scientific article; zbMATH DE number 6330898