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Remarks on some simple $C^*$-algebras admitting a unique lower semicontinuous 2-quasitrace

Volume 165 / 2021

Jacopo Bassi 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.

Authors

  • Jacopo BassiDepartment of Mathematics
    University of Tor Vergata
    Via della Ricerca Scientifica 1
    00133 Roma, Italy
    e-mail

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