Geodesic
Nuclearity and ${\mathrm {CPC}^*}$-Systems
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e59

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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. 
Courtney, Kristin; Winter, Wilhelm. Nuclearity and ${\mathrm {CPC}^*}$-Systems. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e59. doi: 10.1017/fms.2024.123
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