The density problem for self-commutators of unbounded Bergman operators
type: Item
instance of: scholarly article
title: The density problem for self-commutators of unbounded Bergman operators
zbMATH Open document ID: 1085.47037
author: Sherwin Kouchekian
author: James E. Thomson
published in: Integral Equations and Operator Theory
publication date: 2005-06-15T00:00:00Z
review text: If \(G\) is an open subset of the complex plane \(\mathbb C\), let \(\text{Hol}\,(G)\) denote the class of analytic functions on \(G\), and let \(H^\infty(G)\) denote the class of bounded analytic functions on \(G\). If \(\varphi\in\text{Hol}\,(G)\), then the multiplication operator \(M_{\varphi,G}\) is defined by \(M_{\varphi,G}(f)=\varphi f\). The unbounded Bergman operator \(M_{\theta,G}\), with \(\theta(z)= z\), is denoted by \(S\). In the main results of this paper, the authors show that (1) if \(G\) is a simply connected region of finite area, then the Bergman operator \(S\) and its self commutator \([S^*,S]= S^*S- SS^*\) are densely defined; (2) if \(G\) is an open subset of the plane which lies entirely within a sector of angle \({1\over 2}\pi\), then the Bergman operator \(S\) and its self-commutator \(S^*S- SS^*\) are densely defined.
reviewed by: George O. Okikiolu
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 2176179
zbMATH Keywords: unbounded Bergman operators
zbMATH Keywords: density problem
zbMATH Keywords: self-commutator
MaRDI profile type: Publication
full work available at URL: s00020-002-1273-x
OpenAlex ID: W2352099777
DOI: 10.1007/S00020-002-1273-X
description: scientific article; zbMATH DE number 2176179