Strict comparison and stable rank one

2023/01/23 by Huaxin Lin, Lin, Huaxin
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2301.09250

openalex publication_date 2023/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a σ-unital finite simple C^*-algebra which has strict comparison property. We show that if the canonical map Γ from the Cuntz semigroup to certain lower semi-continuous affine functions is surjective, then A has tracial approximate oscillation zero and stable rank one. Equivalently, if A has an almost unperforated and almost divisible Cuntz semigroup, then A has stable rank one and tracial approximate oscillation zero.

Related

• Tracial approximate divisibility and stable rank one
• Ranks of operators in simple C*-algebras
• Unitary groups and augmented Cuntz semigroups of separable simple Z-stable C*-algebras
• Remarks on some simple C^*-algebras admitting a unique lower semicontinuous 2-quasitrace
• Ranks of operators in simple C*-algebras with stable rank one