论文标题
在局部有限的尺寸轨迹上
On locally finite dimensional traces
论文作者
论文摘要
我们部分解决了关于简单C* - 代数上迹线的近似属性的三个开放问题。我们通过证明局部有限的尺寸（LFD）痕迹在简单的C*-Algebras上形成凸的端子，并部分回答了Nate Brown提出的两个问题，并且它们会自动在本地反思性C* - 代数上自动均匀LFD。我们证明，在这种情况下，在这种情况下，在BlackAdar-Kirchberg的意义上，$ c^*_ r（γ）$均匀地说，在Blackadar-Kirchberg的意义上，$ c^*_ r（γ）$均匀的ICC组$γ$的\ c-algebra $ c^*_ r（γ）$均均匀c^*_ r（γ）$是均匀的\ c-Algebra $ c^*_ r（γ）$是强blackadar-kirchberg。这部分回答了布朗提出的另一个公开问题。
We partially resolve three open questions on approximation properties of traces on simple C*-algebras. We partially answer two questions raised by Nate Brown by showing that locally finite dimensional (LFD) traces form a convex set on simple C*-algebras and that they are automatically uniformly LFD on locally reflexive C*-algebras. We prove that all the traces on the reduced \C-algebra $C^*_r(Γ)$ of a discrete amenable ICC group $Γ$ are uniformly LFD, and conclude that $C^*_r(Γ)$ is strong-NF in the sense of Blackadar-Kirchberg in this case. This partially answers another open question raised by Brown.
