发表机构
Chalmers University of Technology; University of Gothenburg（查尔姆斯理工大学; 哥德堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明单非初等C*-代数中算子秩函数的均匀稠密性，由此推出严格比较蕴含几乎可除性及纯性，并应用于证明严格比较蕴含Z-稳定性，从而解决Toms-Winter猜想于近似次齐次情形，并给出精确C*-代数纯性的等价刻画。
AI 中文摘要
对于单的、非初等的C*-代数，我们证明了由算子秩实现的函数的均匀稠密性。由此可知，迹的严格比较迫使几乎可除性，从而推出纯性。作为应用，我们证明对于可分、单、非初等且具有局部有限核维数的C*-代数，严格比较蕴含$\mathcal{Z}$-稳定性。特别地，Toms--Winter猜想对近似次齐次C*-代数成立。更一般地，我们对于具有全局Glimm性质的C*-代数获得秩的均匀稠密性。因此，一个精确C*-代数是纯的当且仅当它具有严格比较以及全局Glimm性质。
英文摘要
For simple, nonelementary C*-algebras, we show uniform density of functions realized as ranks of operators. It follows that strict comparison by traces forces almost divisibility, and hence pureness. As an application, we show that strict comparison implies $\mathcal{Z}$-stability for separable, simple, nonelementary C*-algebras with locally finite nuclear dimension. In particular, the Toms--Winter conjecture holds for approximately subhomogeneous C*-algebras. More generally, we obtain uniform density of ranks for C*-algebras with the Global Glimm Property. Consequently, an exact C*-algebra is pure if and only if it has strict comparison together with the Global Glimm Property.
Comments12 pages
