Nuclearity and CPC*-systems

Kristin Courtney; Wilhelm Winter

doi:10.1017/fms.2024.123

Nuclearity and CPC*-systems

Kristin Courtney, Wilhelm Winter^*

^*Kontaktforfatter

University of Münster

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

Abstract

We write arbitrary separable nuclear C*-algebras as limits of inductive systems of finite-dimensional C^*-algebras with completely positive connecting maps. The characteristic feature of such CPC^*-systems is that the maps become more and more orthogonality preserving. This condition makes it possible to equip the limit, a priori only an operator space, with a multiplication turning it into a C*-algebra. Our concept generalizes the NF systems of Blackadar and Kirchberg beyond the quasidiagonal case.

Originalsprog	Engelsk
Artikelnummer	e59
Tidsskrift	Forum of Mathematics, Sigma
Vol/bind	13
Antal sider	24
ISSN	2050-5094
DOI	https://doi.org/10.1017/fms.2024.123
Status	E-pub ahead of print - 20. mar. 2025

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10.1017/fms.2024.123Licens: CC BY

Open Access VersionForlagets udgivne version, 423 KBLicens: CC BY

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https://arxiv.org/abs/2304.01332

Citationsformater

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TY - JOUR

T1 - Nuclearity and CPC*-systems

AU - Courtney, Kristin

AU - Winter, Wilhelm

PY - 2025/3/20

Y1 - 2025/3/20

N2 - We write arbitrary separable nuclear C*-algebras as limits of inductive systems of finite-dimensional C*-algebras with completely positive connecting maps. The characteristic feature of such CPC*-systems is that the maps become more and more orthogonality preserving. This condition makes it possible to equip the limit, a priori only an operator space, with a multiplication turning it into a C*-algebra. Our concept generalizes the NF systems of Blackadar and Kirchberg beyond the quasidiagonal case.

AB - We write arbitrary separable nuclear C*-algebras as limits of inductive systems of finite-dimensional C*-algebras with completely positive connecting maps. The characteristic feature of such CPC*-systems is that the maps become more and more orthogonality preserving. This condition makes it possible to equip the limit, a priori only an operator space, with a multiplication turning it into a C*-algebra. Our concept generalizes the NF systems of Blackadar and Kirchberg beyond the quasidiagonal case.

KW - Completely positive map

KW - nuclear C-algebra

KW - Order zero maps

KW - inductive limits

UR - https://arxiv.org/abs/2304.01332

U2 - 10.1017/fms.2024.123

DO - 10.1017/fms.2024.123

M3 - Journal article

SN - 2050-5094

VL - 13

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - e59

ER -

Nuclearity and CPC*-systems

Abstract

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