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

研究了由无界C^*-范数构造的^*-代数的无界^*-表示.我们（Bhatt-Inoue-Ogi）证明了从无界C^*-范数构造一类无界^*-表示是可能的，并定义了在该类中表现良好的^*-表示的概念。特别地，我们刻画了良态^*-表示和谱良态^*-表示的存在性。此外，我们还研究了一般无界算子代数（O^*-代数和部分O*-代数）。我们研究了以下问题：（1）由无界C^*-范数构造的良^*-表示的存在性。(2)应用于局部凸^*-代数。(3)具有谱无界C^*-范数的（局部凸）^*-代数的结构和表示理论的研究。(4)谱良^*-表示的存在性。(5)（部分）O^*-代数上的权的研究。(6)（部分）O^*-代数的导子。(7)O^*-代数的条件期望。

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.