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

点击翻译按钮获取中文摘要

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.