Introduction to the flow of weights on factors of type III
Introduction to the flow of weights on factors of type III
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III类因素权重流介绍
DOI：
10.1007/3-540-08853-9_11
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
M. Takesaki
中科院分区：
文献类型：
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作者：
M. Takesaki
Avon Neumann代数的定义是Hilbert空间上的非退化自伴算子代数，它在弱算子拓扑下是封闭的，即在由半范数族诱导的局部凸拓扑下是封闭的：~~ C~ jL：L~ i~ I，~ J. von Neumann的算子代数基本定理说~=~ u其中~。i~ 6 W ~~-：~ for every~ ej~ c~ for any~~~由于~的每个元素都被写为两个自伴元素的线性延拓，自伴算子的谱分解定理断言由其投影生成。也就是说，~的投影形成了一个基本的构建块。事实上，F。默里和冯·诺依曼在他们的开创性工作中集中于分析因子的投影格。根据定义，因子是具有平凡中心的Avon Neumann代数，即~ ri~ Z~ Co
Avon Neumann algebra means, by definition, a non-degenerate self-adjoint algebra~ of operators on a Hilbert space~ which is closed under the weak operator topology, ie closed under the locally convex topology in~ l~(~) induced by the family of semi-norms:~~ C~ jL: L~ i~ I,~~~~ The fundamental theorem of operator algebras due to J. von Neumann says that~=~ u where.~ i~ 6W~~~-:~ for every~ ej~ c~ for any~~~ Since every element of~ is written as a linear continuation of two self-adjoint elements, the spectral decomposition theorem for self-adjoint operators asserts that is generated by its projections. Namely, the projections of~ form a fundamental building block. Indeed, F. Murray and J. von Neumann concentrated, in thier pioneering work, on the analysis of the projection lattice of a factor. A factor is, by definition, avon Neumann algebra with trivial center, ie~ ri~ Z~ Co