Decomposition theorems for unital graph C*-algebras

Abstract

We prove that unital graph C*-algebras often admit a convenient decomposition into amalgamated free products. We use this to give a complete characterization of when a unital graph C*-algebra is residually finite-dimensional and when it is operator norm stable (that is, matricially semiprojective).

We added a new section where we give a complete characterization of when a unital graph C*-algebra is matricially semiprojective. Also our previous result on RFD property is now proved for all unital graph C*-algebras