Nuclearity and ${\mathrm {CPC}^*}$ -Systems
We write arbitrary separable nuclear $\mathrm {C}^*$ -algebras as limits of inductive systems of finite-dimensional $\mathrm {C}^*$ -algebras with completely positive connecting maps. The characteristic feature of such ${\mathrm {CPC}^*}$ -systems is that the maps become more and m...
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| Language: | English |
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001233/type/journal_article |
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| author | Kristin Courtney Wilhelm Winter |
| author_facet | Kristin Courtney Wilhelm Winter |
| author_sort | Kristin Courtney |
| collection | DOAJ |
| description | We write arbitrary separable nuclear
$\mathrm {C}^*$
-algebras as limits of inductive systems of finite-dimensional
$\mathrm {C}^*$
-algebras with completely positive connecting maps. The characteristic feature of such
${\mathrm {CPC}^*}$
-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
$\mathrm {C}^*$
-algebra. Our concept generalizes the NF systems of Blackadar and Kirchberg beyond the quasidiagonal case. |
| format | Article |
| id | doaj-art-ec0d18dd471843fdb97d9889cbf1ed4b |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-ec0d18dd471843fdb97d9889cbf1ed4b2025-08-20T03:42:45ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2024.123Nuclearity and ${\mathrm {CPC}^*}$ -SystemsKristin Courtney0https://orcid.org/0000-0002-3602-8721Wilhelm Winter1https://orcid.org/0009-0006-4158-0875University of Southern Denmark, Department of Mathematics and Computer Science, Campusveg 55, DK-5230 Odense M, Denmark; E-mail:University of Münster, Mathematical Institute, Einsteinstr. 62, DE-48149 Münster, GermanyWe write arbitrary separable nuclear $\mathrm {C}^*$ -algebras as limits of inductive systems of finite-dimensional $\mathrm {C}^*$ -algebras with completely positive connecting maps. The characteristic feature of such ${\mathrm {CPC}^*}$ -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 $\mathrm {C}^*$ -algebra. Our concept generalizes the NF systems of Blackadar and Kirchberg beyond the quasidiagonal case.https://www.cambridge.org/core/product/identifier/S2050509424001233/type/journal_article46L05 |
| spellingShingle | Kristin Courtney Wilhelm Winter Nuclearity and ${\mathrm {CPC}^*}$ -Systems Forum of Mathematics, Sigma 46L05 |
| title | Nuclearity and ${\mathrm {CPC}^*}$ -Systems |
| title_full | Nuclearity and ${\mathrm {CPC}^*}$ -Systems |
| title_fullStr | Nuclearity and ${\mathrm {CPC}^*}$ -Systems |
| title_full_unstemmed | Nuclearity and ${\mathrm {CPC}^*}$ -Systems |
| title_short | Nuclearity and ${\mathrm {CPC}^*}$ -Systems |
| title_sort | nuclearity and mathrm cpc systems |
| topic | 46L05 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001233/type/journal_article |
| work_keys_str_mv | AT kristincourtney nuclearityandmathrmcpcsystems AT wilhelmwinter nuclearityandmathrmcpcsystems |