Locally convex quasi \(^*\)-algebras with sufficiently many \(^*\)-representations
The aim of the authors in this paper is to obtain conditions under which a locally convex quasi \(^*\)-algebra has sufficiently many continuous \(^*\)-representations in an algebra of unbounded operators acting on a Hilbert space to separate its points. They present such conditions which are related to positivity. The results lead to the study of so-called fully representable locally convex quasi \(^*\)-algebras. The authors give several examples of such algebras and study their structure in which the concept of order bounded elements plays a crucial role.
fully representable quasi \(^*\)-algebra
scientific article; zbMATH DE number 6009627
scientific article