Decomposable approximations of nuclear C*-algebras

Abstract

We show that nuclear C*-algebras have a refined version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use this to show that a separable nuclear C*-algebra A which is closely contained in a C*-algebra B embeds into B.

Typos and and a few minor points corrected. Adv. Math., to appear

References in corpus (3)

• Factorization and dilation problems for completely positive maps on von Neumann algebras
• The nuclear dimension of C*-algebras
• Decomposition rank and Z-stability

Cited by in corpus (14)

• Nuclear dimension of simple C*-algebras
• Nuclear dimension and Z-stability
• Decomposition rank of Z-stable C*-algebras
• A simple C*-algebra with finite nuclear dimension which is not Z-stable
• Perturbations of intermediate C*-subalgebras for simple C*-algebras
• Decomposable approximations revisited
• Type II_1 factors satisfying the spatial isomorphism conjecture
• The Cuntz semigroup and stability of close C*-algebras
• Decomposable approximations and approximately finite dimensional C*-algebras
• Almost finiteness, comparison, and tracial $\mathcal{Z}$-stability
• Ulam stability for some classes of C*-algebras
• Decomposing nuclear maps
• Tracial approximation in simple C*-algebras
• A Kadison Kastler row metric and intermediate subalgebras