AN UNBOUNDED GENERALIZATION OF TOMITA's OBSERVABLE ALGEBRAS II. Issue 2 (April 2023)

• Record Type: Journal Article
• Authors: Inoue, Hiroshi
• Is Part Of: Reports on mathematical physics. Volume 91:Issue 2(2023)
• Page Start: 251
• Page End: 276
• Publication Date: 2023-04
• Subjects: Tomita's observable algebras -- O*-algebras -- regular T†-algebras -- (weakly) semisimple T†-algebras -- (strongly) singular T†-algebras -- decomposition of T†-algebras; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(23)00028-9
• Languages: English
• ISSNs: 0034-4877

Abstract

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.