Remarks on 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.

References in corpus (2)

• Reduction of the dimension of nuclear C*-algebras
• Regularity for stably projectionless, simple C*-algebras

Cited by in corpus (2)

• Picard groups of certain stably projectionless C*-algebras
• Unitary orbits of self-adjoint operators in simple Z-stable C*-algebras