On \(C^\ast\)-algebras of Toeplitz operators on the harmonic Bergman space
type: Item
instance of: scholarly article
title: On \(C^\ast\)-algebras of Toeplitz operators on the harmonic Bergman space
zbMATH Open document ID: 1282.47039
author: Maribel Loaiza
author: Carmen Lozano
published in: Integral Equations and Operator Theory
publication date: 2013-06-13T00:00:00Z
review text: Algebras of Toeplitz operators acting on the harmonic Bergman space \(b^2({\mathbb D})\) of the unit disk are studied. \(C^*\)-algebras generated by Toeplitz operators are described in the following three different cases: (1) Toeplitz operators with bounded radial symbols in the elliptic case; (2) Toeplitz operators with piecewise continuous symbols in the parabolic case; (3) Toeplitz operators with piecewise continuous symbols in the hyperbolic case. It is shown that the corresponding Calkin algebras are commutative in the first two cases and not commutative in the last case.
reviewed by: Oleksiy Karlovych
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 31A05
Mathematics Subject Classification ID: 32A36
Mathematics Subject Classification ID: 32A99
Mathematics Subject Classification ID: 47L80
zbMATH DE Number: 6175201
zbMATH Keywords: harmonic function
zbMATH Keywords: Bergman space
zbMATH Keywords: Bergman projection
zbMATH Keywords: anti-Bergman projection
zbMATH Keywords: algebras of Toeplitz operators
MaRDI profile type: Publication
full work available at URL: s00020-013-2046-4
OpenAlex ID: W2026058225
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DOI: 10.1007/S00020-013-2046-4
description: scientific article; zbMATH DE number 6175201