AN UNBOUNDED GENERALIZATION OF TOMITA's OBSERVABLE ALGEBRAS II

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2023-04-01 DOI:10.1016/S0034-4877(23)00028-9

Hiroshi Inoue

引用次数: 2

Abstract

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.

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富田可观测代数的无界推广2

在之前的论文[4]中，我们试图建立与无界算子代数有关的无界富田可观测代数的基本理论，称为T†-代数，特别是无界富田武崎理论、Krein空间上的算子代数、*-代数上的正线性泛函的研究等，T†-代数的半单性和奇异性及其刻画。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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.