Geodesic
Tracial oscillation zero and stable rank one
Canadian journal of mathematics, Tome 77 (2025) no. 2, pp. 563-630

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DOI

Let A be a separable (not necessarily unital) simple $C^*$-algebra with strict comparison. We show that if A has tracial approximate oscillation zero, then A has stable rank one and the canonical map $\Gamma $ from the Cuntz semigroup of A to the corresponding lower-semicontinuous affine function space is surjective. The converse also holds. As a by-product, we find that a separable simple $C^*$-algebra which has almost stable rank one must have stable rank one, provided it has strict comparison and the canonical map $\Gamma $ is surjective.
DOI : 10.4153/S0008414X24000099
Mots-clés : Tracial oscillation zero, stable rank one, Simple C*-algebras 
Fu, Xuanlong; Lin, Huaxin. Tracial oscillation zero and stable rank one. Canadian journal of mathematics, Tome 77 (2025) no. 2, pp. 563-630. doi: 10.4153/S0008414X24000099
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