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10 votes
2 answers
689 views

Stable rank one and corners of $C^\ast$-algebras

Thanks to a result of Herman and Vaserstein in [3], Rieffel's notion of stable rank [4] coincides with the Bass stable rank [1] for every $C^\ast$-algebra $A$: we denote it by $\mathrm{sr}(A)$ and we ...
6 votes
0 answers
233 views

Group $C^*$ vs group von-Neumann algebras

Let $\Gamma$ be a countable (discrete) group (in what follows, make additional assumptions as you wish). Let $C^*_r(\Gamma)$ and $W^*_r(\Gamma)$ be the reduced $C^*$-algebra respectively the reduced ...