Unbounded operator algebras and the applications to the quantum physics

无界算子代数及其在量子物理中的应用

• 批准号: 11640222
• 负责人: INOUE Atsushi
• 金额: $ 1.54万
• 依托单位: FUKUOKA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640222/
• 关键词: O^*-algebras; partial O^*-algebras; weights; standard weights; unbounded Tomita-Takesaki theory; quantum groups; locally convex *-algebras; well-behaved*-表現; 非有界C^*-セミノルム; O^*-台数; PartialO^*-

We have studied unbounded Tomita-Takesaki theory which plays an important role for the structure theory and for applications to the quantum physics in the studies of algebras of unbounded operators (O^*-algebras, partial O^*-algebras). Weights on (partial) O^*-algebras are important for the physical applications (for example, the BCS-models) and for the structure of (partial) O^*-algebras.We have defined the notion of standard weights on (partial) O^*-algebras which is possible to develop the unbounded Tomita-Takesaki theory, and generalized the modular theory, Connes cocycle theorem and Randon-Nikodym theorem for von Neumann algebras to the case of (partial) O^*-algebras. We have tried to apply the existence of Haar measur in the locally compact quantum group.Furthermore, we have investigated weights and unbounded C^*-algebras for the structure theory and the representation theory of (locally convex) *-algebras.

我们研究了无界的tomita-takesaki理论，该理论在结构理论和对量子物理学的应用中起重要作用，在无限算子的代数研究中（O^* - 代数，部分O^* - 代数）。 （部分）O^* - 代数的权重对于物理应用（例如，BCS模型）和（部分）O^* - 代数的结构很重要von Neumann代数定理为（部分）O^* - 代数。我们试图在局部紧凑的量子组中应用HAAR测量值。FurThermore，我们已经研究了结构理论的权重和无界的C^ * - 代数，以及（局部凸） * - 代数的表示理论。

项目成果

A.Inoue,W.Karwowski and H.Ogi: "Standard weights on algebras of unbounded operators"J.Math.Soc.Japan. 51-4. 911-935 (1999)

A.Inoue、W.Karwowski 和 H.Ogi：“无界算子代数的标准权重”J.Math.Soc.Japan。

A.Inoue,W.Karwowski and H.Ogi: "Standard weights on algebras of unbounded operators"Journal of Math.Soc.Japan. 51. 911-936 (1999)

A.Inoue、W.Karwowski 和 H.Ogi：“无界算子代数的标准权重”Journal of Math.Soc.Japan。

A.Inoue and K.D.Kursten: "Trace representation of weights on algebras of unbounded operators"J.Math.Anal.Appl.. 247. 136-155 (2000)

A.Inoue 和 K.D.Kursten：“无界算子代数的权重的迹表示”J.Math.Anal.Appl.. 247. 136-155 (2000)

S.J.Bhatt,A.Inoue and H.Ogi: "Admissibility of Weights on Non-normed *-Algebras"Transactions of the American Mathematical Society. 351(11). 4629-4656 (1999)

S.J.Bhatt、A.Inoue 和 H.Ogi：“非范数 *-代数上权重的可接受性”美国数学会汇刊。

A.Inoue and K.D.Kiirsten: "Trace representation of weights on algebras of unbounded operators"J.Math.Anal.Appl.. 247. 136-155 (2000)

A.Inoue 和 K.D.Kiirsten：“无界算子代数的权重的迹表示”J.Math.Anal.Appl.. 247. 136-155 (2000)