Extensions of stable $C^*$-algebras

Mikael Røordam

doi:10.4171/dm/103

JournalsdmVol. 6pp. 241–246

Extensions of stable $C^{*}$ -algebras

Mikael Røordam
Department of Mathematics University of Copenhagen Universitetsparken 5 2100 Copenhagen Ø Denmark

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Abstract

We show that an extension of two stable $C^{*}$ -algebras need not be stable. More explicitly we find an extension

0 \to C (Z) \otimes K \to A \to K \to 0

for some (infinite dimensional) compact Hausdorff space $Z$ such that $A$ is not stable. The $C^{*}$ -algebra $A$ in our example has an approximate unit consisting of projections.

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Mikael Røordam, Extensions of stable $C^{*}$ -algebras. Doc. Math. 6 (2001), pp. 241–246

DOI 10.4171/DM/103