Inoue, Atsushi Modular systems induced by trace functionals on algebras of unbounded operators. (English) Zbl 0811.47043 J. Math. Phys. 35, No. 1, 435-442 (1994). Summary: The purpose of this article is to study the unbounded Tomita-Takesaki theory by trace functionals on \(O^*\)-algebras, and to apply the results to the algebras associated with the canonical commutation relation, \(pq- qp=-i1\) (CCR-algebras). Cited in 5 Documents MSC: 47L60 Algebras of unbounded operators; partial algebras of operators 47N50 Applications of operator theory in the physical sciences 81T10 Model quantum field theories Keywords:CCR-algebras; unbounded Tomita-Takesaki theory; trace functionals on \(O^*\)-algebras; canonical commutation relation PDFBibTeX XMLCite \textit{A. Inoue}, J. Math. Phys. 35, No. 1, 435--442 (1994; Zbl 0811.47043) Full Text: DOI References: [1] DOI: 10.1016/S0034-4877(71)80002-2 · Zbl 0211.43904 · doi:10.1016/S0034-4877(71)80002-2 [2] DOI: 10.1016/S0034-4877(71)80002-2 · Zbl 0211.43904 · doi:10.1016/S0034-4877(71)80002-2 [3] DOI: 10.1016/0022-247X(68)90175-3 · Zbl 0172.41203 · doi:10.1016/0022-247X(68)90175-3 [4] DOI: 10.1016/0034-4877(72)90013-4 · Zbl 0252.46088 · doi:10.1016/0034-4877(72)90013-4 [5] DOI: 10.1007/BF01220848 · Zbl 0398.47027 · doi:10.1007/BF01220848 [6] DOI: 10.1090/pspum/038.2/679528 · doi:10.1090/pspum/038.2/679528 [7] DOI: 10.1063/1.522605 · Zbl 0316.46062 · doi:10.1063/1.522605 [8] DOI: 10.1063/1.522898 · doi:10.1063/1.522898 [9] DOI: 10.1007/BF02104505 · Zbl 0715.46044 · doi:10.1007/BF02104505 [10] DOI: 10.1007/BF01212341 · Zbl 0595.46062 · doi:10.1007/BF01212341 [11] DOI: 10.1090/S0002-9947-1978-0511398-0 · doi:10.1090/S0002-9947-1978-0511398-0 [12] DOI: 10.1017/S0305004100075460 · Zbl 0771.47025 · doi:10.1017/S0305004100075460 [13] DOI: 10.1002/mana.19921550118 · Zbl 0779.47037 · doi:10.1002/mana.19921550118 [14] DOI: 10.1016/0034-4877(79)90069-7 · Zbl 0447.46051 · doi:10.1016/0034-4877(79)90069-7 [15] Kurose H., Nihonkai Math. J. 1 pp 19– (1990) [16] DOI: 10.2977/prims/1195177629 · Zbl 0624.47044 · doi:10.2977/prims/1195177629 [17] DOI: 10.2977/prims/1195176253 · Zbl 0641.47050 · doi:10.2977/prims/1195176253 [18] DOI: 10.2140/pjm.1977.70.369 · Zbl 0374.46045 · doi:10.2140/pjm.1977.70.369 [19] DOI: 10.1016/0034-4877(72)90012-2 · Zbl 0252.46087 · doi:10.1016/0034-4877(72)90012-2 [20] DOI: 10.1007/BF01646746 · Zbl 0214.14102 · doi:10.1007/BF01646746 [21] DOI: 10.2977/prims/1195179844 · Zbl 0609.47058 · doi:10.2977/prims/1195179844 [22] DOI: 10.2977/prims/1195171084 · Zbl 0724.47020 · doi:10.2977/prims/1195171084 [23] DOI: 10.2977/prims/1195169662 · Zbl 0749.47030 · doi:10.2977/prims/1195169662 [24] DOI: 10.1063/1.529417 · Zbl 0769.47015 · doi:10.1063/1.529417 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.