Weak Exactness for C^*-algebras and Application to Condition (AO}
Weak Exactness for C^*-algebras and Application to Condition (AO}
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C^*-代数的弱精确性及其在条件 (AO} 中的应用
DOI：
10.1016/j.jfa.2012.10.021
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发表时间：
2013
影响因子：
1.7
通讯作者：
Yusuke
中科院分区：
文献类型：
--
作者：
ISONO;Yusuke
Kirchberg引入了von Neumann代数的弱正确度作为C⁎-代数正确度的类比。小泽发现了弱正合度的有用刻画，并证明了群von Neumann代数的弱正合度等价于群的正合度。我们将这一概念推广到von Neumann代数中C-⁎-代数的包含，并研究了它的一些基本性质及其与KirchbergʼS弱正合性的关系。然后，我们给出了一些类似于正合群的持久性性质。在最后一节中，我们研究了一个类似于OzawaʼS条件(AO)的条件，推广了双正合群的OzawaʼS定理。作为推论，我们给出了素因子的新例子。
Kirchberg introduced weak exactness for von Neumann algebras as an analogue of exactness for C⁎-algebras. Ozawa found useful characterizations of weak exactness and he proved that weak exactness for group von Neumann algebras is equivalent to exactness of the groups. We generalize this concept to inclusions of C⁎-algebras in von Neumann algebras and study some fundamental properties and relationship to Kirchbergʼs weak exactness. We then give some permanence properties which are similar to those of exact groups. In the last section, we study a similar condition to Ozawaʼs condition (AO) with our weak exactness and generalize Ozawaʼs theorem for bi-exact groups. As a corollary, we give new examples of prime factors.