Stability of -algebras is not a stable property

  • Mikael Rørdam

Stability of $C^*$-algebras is not a stable property cover
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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.

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Mikael Rørdam, Stability of -algebras is not a stable property. Doc. Math. 2 (1997), pp. 375–386

DOI 10.4171/DM/35