Remarks on Z-stable projectionless C*-algebras

TL;DR

This paper investigates the structure of projectionless Z-stable C*-algebras, showing that elements can be approximated by products of nilpotents and classifying positive elements via traces.

Contribution

It introduces a new approximation property for projectionless Z-stable C*-algebras and provides a trace-based classification of positive elements.

Findings

Every element in such algebras is a limit of products of two nilpotents

Classification of positive elements using traces

Structural insights into Z-stable projectionless C*-algebras

Abstract

It is shown that projectionless C*-algebras that tensorially absorb the Jiang-Su algebra have the property that every element is a limit of products of two nilpotents. This is then used to classify the approximate unitary equivalence classes of positive elements in such C*-algebras using traces.