Decomposable approximations of nuclear C*-algebras

Ilan Hirshberg; Eberhard Kirchberg; Stuart White

doi:https://doi.org/10.1016/j.aim.2012.03.028

Decomposable approximations of nuclear C*-algebras

Ilan Hirshberg, Eberhard Kirchberg, Stuart White

Department of Mathematics

Ben-Gurion University of the Negev

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

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	American 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

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1016/j.aim.2012.03.028

Cite this

@article{13eb8eb055fd4b3cb29a52b2e0eb9b49,

title = "Decomposable approximations of nuclear C*-algebras",

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",

note = "Funding Information: This research was supported by Israel Science Foundation grant 1471/07 and UK Engineering and Physical Sciences Research Council grant EP/I019227/1 .",

year = "2012",

month = jun,

day = "20",

doi = "https://doi.org/10.1016/j.aim.2012.03.028",

language = "American English",

volume = "230",

pages = "1029--1039",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "3",

}

TY - JOUR

T1 - Decomposable approximations of nuclear C*-algebras

AU - Hirshberg, Ilan

AU - Kirchberg, Eberhard

AU - White, Stuart

N1 - Funding Information: This research was supported by Israel Science Foundation grant 1471/07 and UK Engineering and Physical Sciences Research Council grant EP/I019227/1 .

PY - 2012/6/20

Y1 - 2012/6/20

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84860515228&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.aim.2012.03.028

DO - https://doi.org/10.1016/j.aim.2012.03.028

M3 - Article

SN - 0001-8708

VL - 230

SP - 1029

EP - 1039

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 3

ER -

Decomposable approximations of nuclear C*-algebras

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this