Subnormal operators of finite type. II: Structure theorems
type: Item
instance of: scholarly article
title: Subnormal operators of finite type. II: Structure theorems
zbMATH Open document ID: 0933.47016
DOI: 10.4171/RMI/247
author: Dmitry V. Yakubovich
published in: Revista Matemática Iberoamericana
publication date: 2000-04-04T00:00:00Z
full work available at URL: https://eudml.org/doc/39559
review text: In connection with Xia's results for a pure (i.e., it has no normal part) subnormal operator (i.e., it has a normal extension) with finite rank self-commutator, which is called of finite type, the author gives, in this second paper, a complete structure result for subnormal operators of finite type, which corrects and strengthens Xia's formulation. Xia claimed that each subnormal operator of finite type is unitarily equivalent to the multiplicative operator by \(z\) on a weighted vector \(H^2\)-space over a ``quadrature Riemann surface'' (with a finite rank perturbation of the norm). Xia's formula is not accurate, because it would follow from it that every subnormal operator of finite type is simple but there is an example of a subnormal operator of finite type which is not necessarily simple. And the author explains how this formulation can be corrected.
reviewed by: Takashi Yoshino
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 1275455
zbMATH Keywords: quadrature Riemann surface
zbMATH Keywords: normal part
zbMATH Keywords: subnormal
zbMATH Keywords: normal extension
zbMATH Keywords: finite rank self-commutator
zbMATH Keywords: finite type
MaRDI profile type: Publication
OpenAlex ID: W1975705883
description: scientific article; zbMATH DE number 1275455