Decomposable approximations of nuclear C*-algebras

Ilan Hirshberg; Eberhard Kirchberg; Stuart White

doi:10.1016/j.aim.2012.03.028

Decomposable approximations of nuclear C*-algebras

Ilan Hirshberg, Eberhard Kirchberg, Stuart White

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

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.

Original language	English
Pages (from-to)	1029-1039
Number of pages	11
Journal	Advances in Mathematics
Volume	230
Issue number	3
DOIs	https://doi.org/10.1016/j.aim.2012.03.028
State	Published - 20 Jun 2012

Keywords

Decomposition rank
Nuclear C*-algebras
Nuclear dimension

ASJC Scopus subject areas

Mathematics (all)

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10.1016/j.aim.2012.03.028

Cite this

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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.",

keywords = "Decomposition rank, Nuclear C*-algebras, Nuclear dimension",

author = "Ilan Hirshberg and Eberhard Kirchberg and Stuart White",

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AU - White, Stuart

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AB - 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.

KW - Decomposition rank

KW - Nuclear C-algebras

KW - Nuclear dimension

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Decomposable approximations of nuclear C*-algebras

Abstract

Keywords

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