Decomposable approximations of nuclear C*-algebras

Hirshberg, I., Kirchberg, E. and White, S. (2012) Decomposable approximations of nuclear C*-algebras. Advances in Mathematics, 230(3), pp. 1029-1039. (doi:10.1016/j.aim.2012.03.028)

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Abstract

We show that nuclear C*-algebras have a refined version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use this to show that a separable nuclear C*-algebra A which is closely contained in a C*-algebra B embeds into B.

Item Type:Articles
Additional Information:NOTICE: this is the author’s version of a work that was accepted for publication in Advances in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Mathematics 230(3):1029-1039, http://dx.doi.org/10.1016/j.aim.2012.03.028
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:White, Professor Stuart
Authors: Hirshberg, I., Kirchberg, E., and White, S.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
Publisher:Elsevier
ISSN:0001-8708
Published Online:21 April 2012
Copyright Holders:Copyright © 2012 Elsevier
First Published:First published in Advances in Mathematics 230(3):1029-1039
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
596411The Cuntz Semigroup and the Fine Structure of Nuclear C*-AlgebrasStuart WhiteEngineering & Physical Sciences Research Council (EPSRC)EP/I019227/1M&S - MATHEMATICS