Geodesic
Stability of $C^*$-algebras is not a stable property
Documenta mathematica, Tome 2 (1997), pp. 375-386
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We show that there exists a C∗-algebra B such that M2​(B) is stable, but B is not stable. Hence stability of C∗-algebras is not a stable property. More generally, we find for each integer n≥2 a C∗-algebra B so that Mn​(B) is stable and Mk​(B) is not stable when 1≤kC∗-algebras we exhibit have the additional properties that they are simple, nuclear and of stable rank one.
DOI : 10.4171/dm/35
Classification : 19K14, 46L05, 46L35
Mots-clés : stable C∗-algebras, perforation in K0​, scaled ordered abelian groups 
@article{10_4171_dm_35,
     author = {Mikael R{\o}rdam},
     title = {Stability of $C^*$-algebras is not a stable property},
     journal = {Documenta mathematica},
     pages = {375--386},
     year = {1997},
     volume = {2},
     doi = {10.4171/dm/35},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/35/}
}
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Mikael Rørdam. Stability of $C^*$-algebras is not a stable property. Documenta mathematica, Tome 2 (1997), pp. 375-386. doi: 10.4171/dm/35

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