Nuclearity and CPC*-systems

2023/04/03 by Courtney, Kristin, Winter, Wilhelm · 1 citation
#46L05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2304.01332

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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