Weakly exact von Neumann algebras
Weakly exact von Neumann algebras
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DOI：
10.2969/jmsj/05940985
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发表时间：
2004-11
影响因子：
0.7
通讯作者：
Narutaka Ozawa
中科院分区：
文献类型：
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作者：
Narutaka Ozawa
正合C*-代数理论是由基希贝格提出的，在C*-代数的发展中有着重要的影响.关于正合C*-代数的一个基本结果是正合性的局部刻画。弱正合冯诺依曼代数的概念也是由基希贝格提出的。本文给出了弱正合性的一个局部刻画。作为推论，我们证明了一个离散群是正合的当且仅当它的群von Neumann代数是弱正合的。证明自然涉及算子空间对偶。
The theory of exact C*-algebras was introduced by Kirchberg and has been influential in recent development of C*-algebras. A fundamental result on exact C*-algebras is a local characterization of exactness. The notion of weakly exact von Neumann algebras was also introduced by Kirchberg. In this paper, we give a local characterization of weak exactness. As a corollary, we prove that a discrete group is exact if and only if its group von Neumann algebra is weakly exact. The proof naturally involves the operator space duality.