Unbounded *-representations of partial *-algebras

部分*-代数的无界*-表示

• 批准号: 13640228
• 负责人: INOUE Atsushi
• 金额: $ 1.47万
• 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: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640228/
• 关键词: O^*-algebras; partial O^*-algebras; unbounded *-representations; unbounded D^*seminorms; weights; well-behaved *-representations; 非有界C^*-セミノルム; ウエイト

*-algebras (O^*-algebras) of closable operators in Hilbert space have been studied from the pure mathematical situation and the physical applications. A survey of the theory of O^*-algebras may be found in the monograph of K. Schmudgen "Unbounded Operator Algebras and Representation Theory, Operator Theory: Advances and Applications vol. 37, Birkhauser(1990)" and the lecture note of A. Inoue "Tomita-Takasaki Theory in Algebras of Unbounded Operator Algebras, Lecture Notes in Mathematics, 1699, Springer(1995)".Furthermore, partial *-algebras (partial O^*-algebras) of closable operators have been studied from the mathematical situations and the physical applications, but it seems that the systematic studies are insufficient. In order to proceed the studies of *-representations of partial *-algebras, we have investigated the following.(1) What is a well-behaved *-representation in unbounded *-representations of (partial) *-algebras?(2) Systemic studies of weights of partial O^*-algebras.(3) Applications of (1) and (2) to quantum physics.Thus we (A. Inoue, J. P. Antoine and C. Trapani) have published a book "Partial *-algebras and Their Operator Realizations, Mathematics and Its Applications vol. 553" from Kluwer Academic Publishers.

* - 希尔伯特空间中可封闭的操作员的代数（o^* - 代数）已从纯粹的数学情况和物理应用中研究。在K. Schmudgen的专着“无限的操作者代数和代表理论，操作者理论：进步和应用第37卷，1990年，Birkhauser（1990）”中，可以找到对O^* - 代数理论的调查。 Springer（1995）。“此外，已经从数学情况和物理应用中研究了可近可算子的部分 * - 代数（部分O^ * - 代数），但似乎系统研究不足。为了进行部分 * - 代数的 *代表的研究，我们已经调查了以下内容。（1）（1）无限制的 * - 代表 * - （部分） * - 代理的代表是什么？ Inoue，J。P。Antoine和C. Trapani）发表了一本书“部分 * - 代数及其操作员的实现，数学及其应用程序，第553卷”，来自Kluwer学术出版商。

项目成果

井上淳(共著): "On C^*-like locally convex *-algebras"Z. Anal. Anw.. 20. 295-314 (2001)

Jun Inoue（合著者）：“论 C^* 式局部凸 *-代数”Z. Anw.. 20. 295-314 (2001)

A. Inoue: "Unbounded C^*-seminorms and unbounded C^*-spectral algebras"J. Operator Theory. 45. 53-80 (2001)

A. Inoue：“无界 C^*-半范数和无界 C^*-谱代数”J.

井上淳(共著): "Partial *-Algebras and Their Operator Realizations, Mathematics and Its Applications vol.553"Kluwer Academic Publishers. 521 (2002)

Jun Inoue（合著者）：“偏*-代数及其算子实现，数学及其应用第 553 卷”Kluwer 学术出版社 521 (2002)。

井上淳(共著): "Unbounded C^*-seminorms and unbounded C^*-spectral algebras"J. Operator Theory. 45. 53-80 (2001)

Jun Inoue（合著者）：“无界 C^*-半范数和无界 C^*-谱代数”J. 算子理论 45. 53-80 (2001)

井上 淳(共著): "Some clases of topological quasi *-algebras"Proc. Amer. Math. Soc.. 129(to appear). 2973-2980 (2001)

Jun Inoue（合著者）：“拓扑准 *-代数的一些类”Proc. Soc.. 2973-2980（待发表）。