Hankel operators and Toeplitz operators on the Bergman space
type: Item
instance of: scholarly article
title: Hankel operators and Toeplitz operators on the Bergman space
zbMATH Open document ID: 0678.47026
DOI: 10.1016/0022-1236(89)90032-3
published in: Journal of Functional Analysis
publication date: 1989-01-01T00:00:00Z
review text: The author gives several equivalent conditions of compactness of semi- commutator \(T_{\bar fg}-T_{\bar f}T_ g\) of Toeplitz operators with bounded harmonic symbols acting on the Bergman space. As a consequence he proves Axler's conjecture (for bounded analytic functions f and g on the unit disk D the commutator \(T^*_ fT_ g- T_ gT^*_ f\) is compact iff either f or g is constant on each Gleason part P(m) except D).
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47B06
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 4111381
zbMATH Keywords: commutator
zbMATH Keywords: compactness of semi-commutator
zbMATH Keywords: Toeplitz operators with bounded harmonic symbols acting on the Bergman space
zbMATH Keywords: Axler's conjecture
zbMATH Keywords: Gleason part
author: Dechao Zheng
MaRDI profile type: Publication
full work available at URL: 0022-1236(89)90032-3
OpenAlex ID: W1998731180
cites work: The Bergman space, the Bloch space, and commutators of multiplication operators
cites work: Products of Toeplitz operators
cites work: Algebras on the Disk and Doubly Commuting Multiplication Operators
cites work: Q4725177
cites work: Q3922907
cites work: Bounded analytic functions and Gleason parts
cites work: Q3951100
cites work: VMO, ESV, and Toeplitz Operators on the Bergman Space
description: scientific article; zbMATH DE number 4111381