Non-simple purely infinite \(C^{*}\)-algebras: The Hausdorff case.
type: Item
instance of: scholarly article
title: Non-simple purely infinite \(C^{*}\)-algebras: The Hausdorff case.
zbMATH Open document ID: 1048.46049
author: Eberhard Kirchberg
author: Etienne Blanchard
published in: Journal of Functional Analysis
publication date: 2004-03-14T00:00:00Z
review text: Local and global definitions of weak/strong pure infiniteness for a \(C^*\)-algebra \(A\) are compared and equivalence between them is obtained if the primitive ideal space of \(A\) is Hausdorff and finite-dimensional, if \(A\) has real rank zero or if \(A\) is approximately divisible. Sufficient criteria are given for local pure infiniteness of tensor products. It is also shown that \(A\) is isomorphic to \(A\otimes{\mathcal O}_\infty\) if \(A\) is purely infinite separable stable nuclear and if Prim\((A)\) is Hausdorff.
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 19K99
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 2055852
zbMATH Keywords: purely infinite \(C^*\)-algebra
zbMATH Keywords: non-simple \(C^*\)-algebra
reviewed by: Vladimir M. Manuilov
MaRDI profile type: Publication
full work available at URL: j.jfa.2003.06.008
OpenAlex ID: W2108472499
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DOI: 10.1016/J.JFA.2003.06.008
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description: scientific article; zbMATH DE number 2055852