Stability of -algebras is not a stable property
Mikael Rørdam
![Stability of $C^*$-algebras is not a stable property cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-2.png&w=3840&q=90)
Abstract
We show that there exists a -algebra such that is stable, but is not stable. Hence stability of -algebras is not a stable property. More generally, we find for each integer a -algebra so that is stable and is not stable when . The -algebras we exhibit have the additional properties that they are simple, nuclear and of stable rank one.
Cite this article
Mikael Rørdam, Stability of -algebras is not a stable property. Doc. Math. 2 (1997), pp. 375–386
DOI 10.4171/DM/35