Algebraic Aspects in Modular Theory
Algebraic Aspects in Modular Theory
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模块化理论中的代数方面
DOI：
10.2977/prims/1195167738
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发表时间：
1992
影响因子：
1.2
通讯作者：
S. Yamagami
中科院分区：
文献类型：
--
作者：
S. Yamagami
如今，冯诺依曼代数的所谓模理论在算子代数领域已经得到了很好的建立和充分的利用（例如参见[17]）。然而，在某种意义上，传统上使用的符号似乎没有那么多的表现力。本文的主要目的之一是集中讨论算子代数中的这种模理论问题。在过去的一段时间里，已经有一些关于改进模理论符号的建议，但并不彻底。其中，Woronowicz的方法[22]和[2]中引入的新符号值得关注。与此同时，Haagerup、Connes-Hilsum、Kosaki和Araki-Masuda等人提出了任意von Neumann代数的非交换的//-理论，值得指出的是，在这个理论中，von Neumann代数的一个状态的l/p次方与相关的//-空间中的一个元素是一致的。现在我们对这篇文章的内容做一个简要的概述。第一节概述了本文的背景资料，实质部分从下一节开始。
Nowadays, the so called modular theory for von Neumann algebras is well-established and fully utilized (see [17] for example) in the field of operator algebras. The symbols conventionally used there, however, does not seem to be so much expressive in some sense. One of the main purposes in the present article is a focussed account of the problem of this kind for modular theory in operator algebras. In the past time, there had been already some suggestions on the improvement of notations for the modular theory but not in a thorough way. Among them, Woronowicz's approach [22] and new symbols introduced in [2] are worthy of attention. Around the same time of these works, the non-commutative //-theory for arbitrary von Neumann algebras came out and had been developped by several people such as Haagerup, Connes-Hilsum, Kosaki, and Araki-Masuda, and so on. It is worth pointing out the fact that, in this theory, the l/p-th power of a state of a von Neumann algebra is identified with an element in the relevant //-space. Now we give a brief outline of the contents in this article. The first section surveys the background materials and the substantial parts start from the next section.