On subnormal operators
type: Item
instance of: scholarly article
title: On subnormal operators
zbMATH Open document ID: 0605.47022
DOI: 10.1007/BF02837247
author: B. George
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1986-01-01T00:00:00Z
review text: Let S be a pure subnormal operator such that \(C^*(S)\), the \(C^*\)- algebra generated by S, is generated by a unilateral shift U of multiplicity 1. We obtain conditions under which S is unitarily equivalent to \(\alpha +\beta U\), \(\alpha\) and \(\beta\) being scalars or S has \(C^*\)-spectral inclusion property. It is proved that if in addition, S has \(C^*\)-spectral inclusion property, then so does its dual T and \(C^*(T)\) is generated by a unilateral shift of multiplicity 1. Finally, a characterization of quasinormal operators among pure subnormal operators is obtained.
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 3977744
zbMATH Keywords: pure subnormal operator
zbMATH Keywords: \(C^ *\)-algebra
zbMATH Keywords: \(C^ *\)-spectral inclusion property
zbMATH Keywords: unilateral shift of multiplicity 1
zbMATH Keywords: quasinormal operators
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3977744