Remarks on some simple $C^*$-algebras admitting a unique lower semicontinuous 2-quasitrace
Volume 165 / 2021
Colloquium Mathematicum 165 (2021), 53-62
MSC: Primary 46L05.
DOI: 10.4064/cm8171-3-2020
Published online: 17 November 2020
Abstract
Using different descriptions of the Cuntz semigroup and of the Pedersen ideal, it is shown that $\sigma $-unital simple $C^*$-algebras with almost unperforated Cuntz semigroup, a unique lower semicontinuous $2$-quasitrace and whose stabilization has almost stable rank $1$ are either stable or algebraically simple.
