A Class of unbounded ^*-representations constructed from unbounded C^*-seminorms

由无界 C^*-半范数构造的一类无界 ^*-表示

• 批准号: 15540223
• 负责人: INOUE Atsushi
• 金额: $ 1.22万
• 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: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540223/
• 关键词: O^*-algebras; partial O^*-aleebras; unbounded ^*-representations; unbounded C^*-seminorms; well-behaved ^*-representations; spectral unbounded C^*-seminorms; spectral ^*-representations; conditional expectations of O^*-algebras; スペクトル非有界C^*-セミノルム

Unbounded ^*-representations of ^*-algebras constructed from unbounded C^*-seminormLs have been studied. We (Bhatt-Inoue-Ogi) showed that it was possible to construct a class of unbounded ^*-representations from unbounded C^*-seminorms, and defined the notion of well-behaved ^*-representations which is nice in its class. In particular, we have characterized the existence of well-behaved ^*-representations and that of spectral well-behaved ^*-representations. Furthermore, we have proceed studies of general unbounded operator algebras (O^*-algebras and partial O*-algebras). We have investigated the following:(1) The existence of well-behaved ^*-representations constructed from unbounded C^*-seminorms.(2) Applications to locally convex ^*-algebras.(3) The studies of the structure and representation theory of (locally convex) ^*-algebras with spectral unbounded C^*-seminorms.(4) The existence of spectral well-behaved ^*-representations.(5) The study of weights on (partial) O^*-algebras.(6) Derivations of (partial) O^*-algebras.(7) Conditional expectations of O^*-algebras.

已经研究了 ^* - 代数的无限 ^* - 已根据未绑定的c ^* - seminormls构建的代数。我们（Bhatt-inoue-ogi）表明，可以从无限的c ^* - seminorms中构造一类无限制的 ^* - 表示，并定义了表现不错的 ^* - 表示的概念，这在同类中很不错。特别是，我们表征了行为良好的 ^*表示的存在和光谱良好的表现 ^* - 表示。此外，我们还进行了一般无界操作员代数的研究（O^* - 代数和部分O*-ergebras）。我们已经研究了以下内容：（1）存在于无限的c ^* - seminorms构建的良好表现的存在。（2）局部施加到局部凸出 ^* - 代数。（3）（3）（局部convex） ^* - 与频谱无基型C ^* - seminems的结构和表示理论的研究（局部convex） ^* - seminormem。（4）。 ^* - 表示。（5）对（部分）O^* - 代数的权重的研究（6）（部分）O^* - 代数的推导。（7）O^* - 代数的条件期望。

项目成果

井上 淳, 高倉真由美: "Radon-Nikodym theorem for biweights and regular biweights on partial *-algebras"Rendiconti del Circolo Mathematico di Palermo. 52. 489-504 (2003)

Jun Inoue，Mayumi Takakura：“偏 *-代数上的二重和正则二重的 Radon-Nikodym 定理”Rendiconti del Circolo Mathematico di Palermo 52. 489-504 (2003)

On structure of locally convex *-algebras with normal unbounded C^*-norms

具有正态无界 C^*-范数的局部凸*-代数的结构

• 发表时间: 2005
• 期刊: Kyushu J.Math. 59
• 作者: A.Inoue;N.Takeshita
• 通讯作者: N.Takeshita

On structure of locally convex ^*-algebras with normal unbounded C^*-norms

具有正态无界 C^*-范数的局部凸 ^*-代数的结构

• 发表时间: 2005
• 期刊: Kyushu J. Math. 59
• 作者: A.Inoue;N.Takeshita
• 通讯作者: N.Takeshita

井上 淳(共著): "Well-behaved unbounded operator representations and unbounded C^*-seminorms"J.Math.Soc.Japan. (to appear).

Jun Inoue（合著者）：“行为良好的无界算子表示和无界 C^*-seminorms”J.Math.Soc.Japan（即将出现）。

井上 淳(共著): "Trace representation of positive invariant sesquilinear forms in partial O^*-algebras"Rendiconti del Circolo Mathematico di Palermo. (to appear).

Jun Inoue（合著者）：“偏 O^*-代数中正不变倍半线性形式的迹线表示”Rendiconti del Circolo Mathematico di Palermo（即将出现）。