CP-stability and the local lifting property

TL;DR

This paper explores the local lifting property in C*-algebras through the lens of CP-stability, an approximation property introduced to facilitate the study of continuous model theory in operator algebras.

Contribution

It establishes an equivalence between the local lifting property and CP-stability, providing a new perspective for analyzing C*-algebras and operator systems.

Findings

CP-stability is equivalent to the local lifting property

The paper offers a new approximation-based approach to study C*-algebras

Facilitates the application of continuous model theory to operator systems

Abstract

The purpose of this note is to discuss the local lifting property in terms of an equivalent approximation-type property, CP-stability, which was formulated by the author and Isaac Goldbring for the purposes of studying the continuous model theory of C$^*$-algebras and operator systems.