English

Nuclearity and CPC*-systems

Operator Algebras 2024-10-10 v2

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.

Keywords

Cite

@article{arxiv.2304.01332,
  title  = {Nuclearity and CPC*-systems},
  author = {Kristin Courtney and Wilhelm Winter},
  journal= {arXiv preprint arXiv:2304.01332},
  year   = {2024}
}

Comments

Corrected minor typos. This version to appear in Forum. Math. Sigma. 31 pages

R2 v1 2026-06-28T09:47:45.127Z