Irreducible representations of inner quasidiagonal C*-algebras

TL;DR

This paper characterizes inner quasidiagonal C*-algebras via quasidiagonal irreducible representations and explores their properties, linking nuclearity and the strong NF algebra class.

Contribution

It provides a new characterization of inner quasidiagonal C*-algebras using separating families of quasidiagonal irreducible representations.

Findings

A separable C*-algebra is inner quasidiagonal iff it has a separating family of quasidiagonal irreducible representations.

A separable C*-algebra is a strong NF algebra iff it is nuclear and has a separating family of quasidiagonal irreducible representations.

The paper establishes permanence properties of inner quasidiagonal C*-algebras.

Abstract

It is shown that a separable C*-algebra is inner quasidiagonal if and only if it has a separating family of quasidiagonal irreducible representations. As a consequence, a separable C*-algebra is a strong NF algebra if and only if it is nuclear and has a separating family of quasidiagonal irreducible representations. We also obtain some permanence properties of the class of inner quasidiagonal C*-algebras.