| Von Neumann代数中的Kakutani定理 |
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| 引用本文： | 魏国强,黄勇.Von Neumann代数中的Kakutani定理[J].华东师范大学学报(自然科学版),1993(4):13-23. |
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| 作者姓名： | 魏国强 黄勇 |
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| 作者单位： | 华东师范大学数学系，华东师范大学数学系 |
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| 摘 要： | 本文定义了Ｖｏｎ Ｎｅｕｍａｎｎ代数态空间上的Ｋａｋｕｔａｎｉ内积。证明了这个内积具有半可乘性并可用它来度量态的奇异程度。此外，又证明了每个超有限Ｖｏｎ Ｎｅｕｍａｎｎ代数存在不可数多个两两正交的态。
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| 关 键 词： | 态 Kakutani定理 诺伊曼代数 |
Kakutani Theorem in Von Neumann Algebras |
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| WEI GUOQIAN,HUANG YONG.Kakutani Theorem in Von Neumann Algebras[J].Journal of East China Normal University(Natural Science),1993(4):13-23. |
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| Authors: | WEI GUOQIAN HUANG YONG |
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| Institution: | WEI GUOQIAN;HUANG YONG Department of Mathematics |
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| Abstract: | The Kakutani inner product on the state space of von Neumann algebras is defined and some of its properties are investigated.It turns out that the Kakutani inner product has the property of semi-multiplicative and it can be used to meas- ure the singular degree of states.Moreover,it is showed that for every hypofinite von Neumann algebra there exists a family of uncountably many states which are pairwise orthogonal. |
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| Keywords: | Von Neumann algebra state singular degsee |
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