Products of Hankel and Toeplitz operators on the Bergman space
type: Item
instance of: scholarly article
title: Products of Hankel and Toeplitz operators on the Bergman space
zbMATH Open document ID: 0945.47019
author: Karel Stroethoff
author: Dechao Zheng
published in: Journal of Functional Analysis
publication date: 2000-10-10T00:00:00Z
review text: Let \(L^2_\alpha\) denote the Bergman space consisting of the analytic functions in \(L^2(D, dA)\), where \(dA\) is the normalized Lebesgue area measure on the unit disk \(D\). Let \(P\) be the orthogonal projection from \(L^2(D, dA)\) onto \(L^2_\alpha\). For \(f\in L^2(D, dA)\), the Toeplitz operator \(T_f\) and the Hankel operator \(H_f\) with symbol \(f\) are defined densely on \(L^2_\alpha\) by \(T_f(h)= P(fh)\) and \(H_f(h)= (1- P)(fh)\) for all polynomials \(h\). The authors consider the question for which \(f\) and \(g\) in \(L^2_\alpha\) the densely defined products \(T_fT_g\) are bounded on the Bergman space. Hankel products \(H_f H^*_g\) and the mixed Haplitz products \(H_fT_g\) and \(T_gH^*_f\) are also investigated. In particular, conditions for compactness of the various Haplitz products are established.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 1398382
zbMATH Keywords: Bergman space
zbMATH Keywords: orthogonal projection
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: Hankel operator
zbMATH Keywords: Hankel products
zbMATH Keywords: Haplitz products
MaRDI profile type: Publication
full work available at URL: jfan.1999.3489
OpenAlex ID: W1995535382
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DOI: 10.1006/JFAN.1999.3489
description: scientific article; zbMATH DE number 1398382