Sums of Toeplitz products with harmonic symbols
type: Item
instance of: scholarly article
title: Sums of Toeplitz products with harmonic symbols
zbMATH Open document ID: 1148.47024
DOI: 10.4171/RMI/529
author: Boo Rim Choe
author: Hyungwoon Koo
author: Young Joo Lee
published in: Revista Matemática Iberoamericana
publication date: 2008-08-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1216247095
full work available at URL: https://eudml.org/doc/42366
review text: The authors study special combinations of Toeplitz operators with bounded harmonic symbols acting on the Bergman space over the unit disk. Let \(h^{\infty}\) be the set of all bounded harmonic functions on the unit disk. The main result of the paper gives criteria for being of finite rank or compact for an operator of the form \[ T=T_{\lambda}+\sum_{j=1}^{N}T_{u_j}T_{v_j}, \] where \(\lambda\) is a finite sum of finite products of functions from \(h^{\infty}\) and \(u_j,\, v_j \in h^{\infty}\) for each \(j\). Some interesting special forms and examples of the operator \(T\) are considered as well.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 32A36
zbMATH DE Number: 5307127
zbMATH Keywords: Bergman space
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: harmonic symbol
zbMATH Keywords: finite rank operator
MaRDI profile type: Publication
cites work: On the range of the Berezin transform
cites work: A theorem of Brown-Halmos type for Bergman space Toeplitz operators
cites work: \(\mathcal M\)-harmonic products
cites work: Commuting Toeplitz operators with harmonic symbols
cites work: Compact operators via the Berezin transform
cites work: Commuting Toeplitz operators on the polydisk
cites work: Pluriharmonic symbols of commuting Toeplitz operators
cites work: Pluriharmonic symbols of essentially commuting Toeplitz operators
cites work: Products of Bergman space Toeplitz operators on the polydisk
cites work: A Lipschitz estimate for Berezin’s operator calculus
cites work: Finite rank commutators and semicommutators of Toeplitz operators with harmonic symbols
cites work: Q4490700
cites work: Bounded analytic functions and Gleason parts
cites work: Q3958740
cites work: Essentially Commuting Toeplitz Operators With Harmonic Symbols
cites work: Hankel operators and Toeplitz operators on the Bergman space
OpenAlex ID: W1968748771
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description: scientific article; zbMATH DE number 5307127