The completion of the maximal \(Op^ *\)-algebra on a Frechet domain
The completion \({\mathcal L}\) of the maximal Op\({}^*\)-algebra \({\mathcal L}^{\dag}({\mathcal D})\) relative to the uniform topology is considered. The author has shown that if \({\mathcal D}\) is a Fréchet space relative to the graph topology for \({\mathcal L}^{\dag}({\mathcal D})\), then so is the space \({\mathcal L}({\mathcal D},{\mathcal D}^{\dag})\) of continuous linear operators of \({\mathcal D}\) into the strong dual \({\mathcal D}^{\dag}\) of \({\mathcal D}\), equipped with the complex conjugate linear structure. From this point of view he has investigated the properties of this space \({\mathcal L}({\mathcal D},{\mathcal D}^{\dag})\) in detail, and shown that \({\mathcal L}({\mathcal D},{\mathcal D}^{\dag})\) is an ordered locally convex space with an involution and a partially defined multiplication. Further, he has given a counterexample to the distributivity property of closed operators, which has influenced a study of partial *-algebras.
ordered locally convex space with an involution
counterexample to the distributivity property of closed operators
scientific article; zbMATH DE number 3981891
scientific article