The general Stone-Weierstrass problem and extremal completely positive maps
type: Item
instance of: scholarly article
title: The general Stone-Weierstrass problem and extremal completely positive maps
zbMATH Open document ID: 0614.46047
DOI: 10.1007/BF01180773
author: John W. Bunce
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155175
review text: The general Stone-Weierstrass conjecture for unital \(C^*\)-algebras \(B\subseteq A\) states that \(A=B\) if B separates the pure states of A. The author proves that the condition of B separating the pure states of A is equivalent to B separating the set of extremal completely positive unital maps of A into L(H) for any finite dimensional Hilbert space H. Furthermore he proves that \(B=A\) if this condition holds for any Hilbert space H with dim \(H\leq card(S)\), the cardinality of some dense subset S of A.
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 3994305
zbMATH Keywords: Stone-Weierstrass conjecture for unital \(C^ *\)-algebras
zbMATH Keywords: separates the pure states
zbMATH Keywords: separating the set of extremal completely positive unital maps
zbMATH Keywords: cardinality
MaRDI profile type: Publication
cites work: Q3966642
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description: scientific article; zbMATH DE number 3994305