Partial \({}^*\)-algebras of closable operators. I: The basic theory and the abelian case
type: Item
instance of: scholarly article
title: Partial \({}^*\)-algebras of closable operators. I: The basic theory and the abelian case
zbMATH Open document ID: 0724.47020
author: Camillo Trapani
author: J. P. Antoine
author: A. Inoue
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1990-01-01T00:00:00Z
review text: This paper is devoted to a systematic study of partial *-algebras of closable operators in a Hilbert space (partial \(Op^*\)-algebras) and to the development of a theory of representations of abstract partial *- algebras, following the pattern familiar to *-algebras. The basic theory of partial *-algebras of closable operators on a Hilbert space is reviewed. The authors also define a new kind of bounded commutant, called quasi-weak. They initiate a theory of abelian partial *-algebras and give a thorough analysis of the partial \(Op^*\)-algebras generated by a single symmetric operator and their bounded commutants.
Mathematics Subject Classification ID: 47L60
Mathematics Subject Classification ID: 46K05
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 4194519
zbMATH Keywords: partial *-algebras of closable operators in a Hilbert space
zbMATH Keywords: partial \(Op^ *\)-algebras
zbMATH Keywords: representations of abstract partial *-algebras
zbMATH Keywords: bounded commutant
zbMATH Keywords: quasi-weak
zbMATH Keywords: abelian partial *-algebras
zbMATH Keywords: partial \(Op^ *\)-algebras generated by a single symmetric operator and their bounded commutants
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195171084
OpenAlex ID: W2046364905
cites work: Q3854185
cites work: Strongly Cyclic Vectors for PartialOp*-Algebras
cites work: Q3327214
cites work: Q3834575
DOI: 10.2977/PRIMS/1195171084
description: scientific article; zbMATH DE number 4194519