Remarks on Z-stable projectionless C*-algebras
Leonel Robert

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.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Noncommutative and Quantum Gravity Theories
