Schatten class Toeplitz operators on the Bergman space
type: Item
instance of: scholarly article
title: Schatten class Toeplitz operators on the Bergman space
zbMATH Open document ID: 1186.47022
DOI: 10.1155/2009/921324
author: Namita Das
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2010-04-20T00:00:00Z
full work available at URL: https://eudml.org/doc/228362
review text: Summary: We show that if the Toeplitz operator \(T_\varphi\) on the Bergman space \(La^2(\mathbb D)\) belongs to the Schatten class \(S^p\), \(1\leq p<\infty\), then \(\widetilde{\varphi}\in L^p(\mathbb D,d\lambda)\), where \(\widetilde{\varphi}\) is the Berezin transform of \(\varphi\), \(d\lambda(z)= dA(z)/(1-|z|^2)^2\), and \(dA(z)\) is the normalized area measure on the open unit disk \(\mathbb D\). Further, if \(\varphi\in L^p(\mathbb D,d\lambda)\), then \(\widetilde{\varphi}\in L^p(\mathbb D,d\lambda)\) and \(T_\varphi\in S^p\). For certain subclasses of \(L^\infty(\mathbb D)\), necessary and sufficient conditions characterizing Schatten class Toeplitz operators are also obtained.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 30H20
zbMATH DE Number: 5695234
Wikidata QID: Q58648527
MaRDI profile type: Publication
OpenAlex ID: W2152714802
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description: scientific article; zbMATH DE number 5695234