A note on $C^*$-algebras with Lifting Property

TL;DR

This paper discusses properties of $C^*$-algebras related to the lifting property, providing simple complements and clarifying the relationship between local lifting property and lifting property for max-contractions.

Contribution

It offers new insights into the relationship between LLP and LP in $C^*$-algebras, simplifying previous results and clarifying their implications.

Findings

LLP associated with max-contractions implies LP for max-contractions

Provides simple complements to previous work on $C^*$-algebras with LP

Clarifies the relationship between local and global lifting properties

Abstract

We give several simple and easy complements to our recent paper on $C^*$-algebras with the lifting property (LP in short). In particular we observe that the local lifting property (LLP in short) associated to the class of max-contractions implies the lifting property for max-contractions.