Geodesic
Stability of $C^*$-algebras is not a stable property
Documenta mathematica, Tome 2 (1997), pp. 375-386.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We show that there exists a $C^*$-algebra $B$ such that $M_2(B)$ is stable, but $B$ is not stable. Hence stability of $C^*$-algebras is not a stable property. More generally, we find for each integer $n \ge 2$ a $C^*$-algebra $B$ so that $M_n(B)$ is stable and $M_k(B)$ is not stable when $1 \le k n$. The $C^*$-algebras we exhibit have the additional properties that they are simple, nuclear and of stable rank one.
Classification : 46L05, 46L35, 19K14
Keywords: stable $C^*$-algebras, perforation in $K_0$, scaled ordered abelian groups 
@article{DOCMA_1997__2__a0,
     author = {R{\o}rdam, Mikael},
     title = {Stability of $C^*$-algebras is not a stable property},
     journal = {Documenta mathematica},
     pages = {375--386},
     publisher = {mathdoc},
     volume = {2},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1997__2__a0/}
}
TY  - JOUR
AU  - Rørdam, Mikael
TI  - Stability of $C^*$-algebras is not a stable property
JO  - Documenta mathematica
PY  - 1997
SP  - 375
EP  - 386
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_1997__2__a0/
LA  - en
ID  - DOCMA_1997__2__a0
ER  - 
%0 Journal Article
%A Rørdam, Mikael
%T Stability of $C^*$-algebras is not a stable property
%J Documenta mathematica
%D 1997
%P 375-386
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_1997__2__a0/
%G en
%F DOCMA_1997__2__a0
Rørdam, Mikael. Stability of $C^*$-algebras is not a stable property. Documenta mathematica, Tome 2 (1997), pp. 375-386. http://geodesic.mathdoc.fr/item/DOCMA_1997__2__a0/