Xia's analytic model of a subnormal operator and its applications
type: Item
instance of: scholarly article
title: Xia's analytic model of a subnormal operator and its applications
zbMATH Open document ID: 1167.47017
DOI: 10.1216/RMJ-2008-38-3-849
author: Jim Gleason
author: C. Ray Rosentrater
published in: Rocky Mountain Journal of Mathematics
publication date: 2009-04-07T00:00:00Z
review text: The present paper gives a nice exposition on subnormal operators, presenting in an attractive form the analytic model of \textit{D.--X.\,Xia} [Integral Equations Oper.\ Theory 10, 258--289 (1987; Zbl 0645.47020)] and its applications. New proofs of some results are given and many examples to help clarify the model are provided. Each section is concluded with a paragraph of notes and open problems, which gives some additional background to the topics covered in the section and some related open problems. One of the basic results in operator theory is the spectral theorem for normal operators. Characterizations of such a type have been given for the theory of Hilbert space contractions. In the second section of the paper, the authors review the effort made towards this end for subnormal operators. Xia's analytic model is presented and some of the complete unitary invariants for pure subnormal operators are described. The third main section of the paper explores these unitary invariants when the self-commutator is of finite rank. A~study of the one-dimensional and the two-dimensional case is made, and a classification of subnormal operators of finite type is presented.
reviewed by: Ilie Valuşescu
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47A45
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47-02
zbMATH DE Number: 5541248
zbMATH Keywords: subnormal operators
zbMATH Keywords: analytic model
zbMATH Keywords: mosaic
zbMATH Keywords: invariants
zbMATH Keywords: finite rank self-commutator
MaRDI profile type: Publication
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Xia's analytic model of a subnormal operator and its applications (full work available at URL)
full work available at URL: rmj-2008-38-3-849

Xia's analytic model of a subnormal operator and its applications (OpenAlex ID)
OpenAlex ID: W2039420873

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