The completion of the maximal \(Op^ *\)-algebra on a Frechet domain
type: Item
instance of: scholarly article
title: The completion of the maximal \(Op^ *\)-algebra on a Frechet domain
zbMATH Open document ID: 0607.47043
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 47L60
Mathematics Subject Classification ID: 46A32
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46A04
zbMATH DE Number: 3981891
zbMATH Keywords: Op\({}^ *\)-algebra
zbMATH Keywords: Fréchet space
zbMATH Keywords: graph topology
zbMATH Keywords: ordered locally convex space with an involution
zbMATH Keywords: counterexample to the distributivity property of closed operators
zbMATH Keywords: partial *-algebras
author: K.-D. Kürsten
reviewed by: Ayumu Inoue
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195178378
OpenAlex ID: W2128957345
cites work: Q4126914
cites work: Some examples of $\left( F \right)$ and $\left( {DF} \right)$ spaces
cites work: Q3679765
cites work: Partial *-algebras of closed linear operators in Hilbert space
cites work: On a certain class of *-algebras of unbounded operators
cites work: On representing \(F^ *\)-algebras
cites work: Generalized B-Algebras
cites work: Q4189689
cites work: Some spectral properties in algebras of unbounded operators
cites work: Homomorphisms and direct sums of nested Hilbert spaces
cites work: A class of unbounded operator algebras
cites work: Q3345273
cites work: Q3927737
cites work: Q5526485
cites work: Q5511567
cites work: Q3207571
cites work: Q3952693
cites work: Q3333606
cites work: Two-Sided Closed Ideals of Certain Algebras of Unbounded Operators
cites work: Topological algebras of operators
cites work: Q3941916
cites work: Algebras of unbounded operators and quantum dynamics
cites work: Q3702837
cites work: Classification of domains of operator algebras
cites work: Q4136031
cites work: Lokal multiplikativ konvexe Op*-Algebren
cites work: On trace representation of linear functionals on unbounded operator algebras
cites work: Uniform topologies on enveloping algebras
cites work: On topologization of unbounded operator algebras
cites work: Q3873052
DOI: 10.2977/PRIMS/1195178378
description: scientific article; zbMATH DE number 3981891