Bicommutants of Toeplitz operators
type: Item
instance of: scholarly article
title: Bicommutants of Toeplitz operators
zbMATH Open document ID: 1168.47026
published in: Archiv der Mathematik
publication date: 2009-01-29T00:00:00Z
review text: A Toeplitz operator \(T_f\) is said to be quasihomogeneous (of order \(p\)) if its symbol \(f\) is of the form \(f(r e^{i \theta})=e^{i p \theta} \varphi (r)\), where \(\varphi\) is a radial function and \(p\) is an integer. Within the context of Toeplitz operators on the Bergman space on the unit disk, it is proven that if two Toeplitz operators commute with a quasihomogeneous Toeplitz operator, then they commute with each other. This is an interesting unexpected phenomenon, quite different from the well-known theorem by Brown and Halmos on commuting Toeplitz operators on the Hardy space.
reviewed by: Pedro J. Paúl
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47L80
zbMATH DE Number: 5500573
zbMATH Keywords: Toeplitz operators
zbMATH Keywords: Bergman space
zbMATH Keywords: bicommutant
author: Issam Louhichi
author: Nagisetty V. Rao
MaRDI profile type: Publication
full work available at URL: s00013-008-2790-x
OpenAlex ID: W2135708544
DOI: 10.1007/S00013-008-2790-X
description: scientific article; zbMATH DE number 5500573