Compact Toeplitz operators for weighted Bergman spaces on bounded symmetric domains
type: Item
instance of: scholarly article
title: Compact Toeplitz operators for weighted Bergman spaces on bounded symmetric domains
zbMATH Open document ID: 1236.32001
author: Hassan Issa
published in: Integral Equations and Operator Theory
publication date: 2011-11-08T00:00:00Z
review text: For an irreducible bounded symmetric domain \(\Omega \) in \({\mathbb C}^d\) the author studies Toeplitz operators \(T_f^{\nu }\) acting on the weighted Bergman space \(H_{\nu } ^2(\Omega )\) with weight \(\nu \), i.e. the space of holomorphic functions in \(L^2(\Omega ,\mu _{\nu })\). The symbol \(f\) is a bounded function on \(\Omega \) and \(T_f^{\nu }=P_{\nu }M_f\), where \(M_f\) is the multiplication by \(f\) and \(P_{\nu }\) the orthogonal projection onto \(H_{\nu } ^2(\Omega )\). The first result is about a comparison of the norm \(\|T_f^{\nu }\|\) with the \(L^{\infty }(\Omega )\)-norm of the Berezin transform of \(f\). As a consequence it is proven that, for \(\nu \) large enough, the compactness of the operator \(T_f^{\nu }\) is independent of the weight \(\nu \).
reviewed by: Jacques Faraut
Mathematics Subject Classification ID: 32A36
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 5969179
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: Berezin transform
MaRDI profile type: Publication
full work available at URL: s00020-011-1885-0
OpenAlex ID: W2067689016
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DOI: 10.1007/S00020-011-1885-0
description: scientific article; zbMATH DE number 5969179