Nuclearity and CPC*-systems

Kristin Courtney; Wilhelm Winter

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arXiv · 2304.01332

Nuclearity and CPC*-systems

Kristin Courtney·Wilhelm Winter

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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.

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Kristin Courtney, Wilhelm Winter. 2023-04-03. Nuclearity and CPC*-systems. https://arxiv.org/abs/2304.01332

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