In a previous paper [4] we tried to build the basic theory of unbounded Tomita's observable algebras called T^†-algebras which are related to unbounded operator algebras, especially unbounded Tomita-Takesaki theory, operator algebras on Krein spaces, studies of positive linear functionals on *-algebras and so on. And we defined the notions of regularity, semisimplicity and singularity of T^†-algebras and characterized them. In this paper we shall proceed further with our studies of T^†-algebras and investigate whether a T^†-algebra is decomposable into a regular part and a singular part.

中文翻译：

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富田可观察代数 II 的无界推广

在之前的一篇论文[4]中，我们试图建立无界 Tomita 的可观测代数的基础理论，称为T ^{† -}代数，它与无界算子代数有关，特别是无界 Tomita-Takesaki 理论，Kerin 空间上的算子代数，正线性泛函的研究*-代数等。定义了T ^{† -代数的正则性、}半单纯性和奇异性的概念并刻画了它们。在本文中，我们将进一步研究T ^† -代数，并研究T ^{† -}代数是否可分解为正则部分和奇异部分。