English

Strict comparison and stable rank one

Operator Algebras 2024-02-21 v2

Abstract

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

Keywords

Cite

@article{arxiv.2301.09250,
  title  = {Strict comparison and stable rank one},
  author = {Huaxin Lin},
  journal= {arXiv preprint arXiv:2301.09250},
  year   = {2024}
}

Comments

revision, removing some typos

R2 v1 2026-06-28T08:17:30.487Z