Tracial algebras and an embedding theorem
Tracial algebras and an embedding theorem
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迹线代数和嵌入定理
DOI：
10.1016/j.jfa.2010.08.010
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Andreas Berthold Thom
中科院分区：
文献类型：
--
作者：
Tim Netzer;Andreas Berthold Thom
证明了可数生成的代数上的每一个正迹都可以用一般矩阵代数上的正迹来逼近。这意味着每一个可数生成的迹代数都可以嵌入到一般矩阵代数的度量超积中。作为一个特殊的结果，每个具有可分预对偶的有限von Neumann代数都可以嵌入迹-代数的超积中，迹-代数作为迹-代数嵌入交换代数上的矩阵环中。
We prove that every positive trace on a countably generated ∗-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial ∗-algebra can be embedded into a metric ultraproduct of generic matrix algebras. As a particular consequence, every finite von Neumann algebra with separable pre-dual can be embedded into an ultraproduct of tracial ∗-algebras, which as ∗-algebras embed into a matrix-ring over a commutative algebra.