A note on when amenable traces are quasidiagonal

TL;DR

This paper proves that for certain separable exact C*-algebras, the property of all amenable traces being quasidiagonal remains unchanged under homotopy transformations.

Contribution

It establishes the homotopy invariance of the quasidiagonality of amenable traces in separable exact C*-algebras.

Findings

Amenable traces are quasidiagonal in the studied class.

Homotopy invariance of this property is demonstrated.

Results contribute to understanding trace properties in operator algebras.

Abstract

We will show that for a separable exact $C^*$-algebra with a faithful amenable trace, the property that all amenable traces are quasidiagonal is invariant under homotopy.