Decomposable approximations of nuclear C*-algebras

TL;DR

This paper introduces a refined approximation property for nuclear C*-algebras, showing they can be approximated by convex combinations of order zero maps, and uses this to establish embedding results.

Contribution

It presents a new decomposable approximation property for nuclear C*-algebras involving convex combinations of order zero maps.

Findings

Nuclear C*-algebras have a refined approximation property.

Separable nuclear C*-algebras can embed into larger C*-algebras under certain conditions.

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.