We prove that Cuntz semigroups of C*-algebras satisfy Edwards' condition with respect to every quasitrace. This condition is a key ingredient in the study of the realization problem of functions on the cone of quasitraces as ranks of positive elements. In the course of our investigation, we identify additional structure of the Cuntz semigroup of an arbitrary C*-algebra and of the cone of quasitraces.

中文翻译：

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C*-代数上拟迹的 Edwards 条件

我们证明了 Cuntz 半群C*-代数关于每个拟迹满足 Edwards 条件。这个条件是研究拟迹锥上的函数实现问题的一个关键因素，作为正元素的秩。在我们的调查过程中，我们确定了任意的 Cuntz 半群的附加结构C*-代数和拟迹锥的。