On the regularity of the partial \(O^*\)-algebras generated by a closed symmetric operator
type: Item
instance of: scholarly article
title: On the regularity of the partial \(O^*\)-algebras generated by a closed symmetric operator
zbMATH Open document ID: 0812.47047
author: Camillo Trapani
author: J. P. Antoine
author: A. Inoue
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1995-05-09T00:00:00Z
review text: Summary: Let \(\mathcal D\) be a given dense domain in a Hilbert space and \(T\) a closed symmetric operator with domain containing \(\mathcal D\). Then the restriction of \(T\) to \(\mathcal D\) generates (algebraically) two partial *-algebras of closable operators (called weak and strong), possibly non-Abelian and nonassociative. We characterize them completely. In particular, we examine under what conditions they are regular, that is, consist of polynomials only, and standard. Simple differential operators provide concrete examples of all the pathologies allowed by the abstract theory.
Mathematics Subject Classification ID: 47L60
zbMATH DE Number: 597473
zbMATH Keywords: partial \(O^*\)-algebras generated by a closed symmetric operator
zbMATH Keywords: regularity
zbMATH Keywords: closed symmetric operator
zbMATH Keywords: partial *-algebras of closable operators
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195167935
OpenAlex ID: W1965507147
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DOI: 10.2977/PRIMS/1195167935
description: scientific article; zbMATH DE number 597473