Von Neumann代数中的Kakutani定理  

Kakutani Theorem in Von Neumann Algebras

作　　者：魏国强[1] 黄勇[1] 

机构地区：[1]华东师范大学数学系

出　　处：《华东师范大学学报（自然科学版）》1993年第4期13-23,共11页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金资助

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。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.

关 键 词：态 Kakutani定理 诺伊曼代数 

分 类 号：O174[理学—数学]