Approximation and the n-Berezin transform of operators on the Bergman space

To any bounded operator S on the Bergman space La2 we associate a sequence of linear transforms Bn(S ) ∈ L∞(D), where n ≧ 0, and prove that the Toeplitz operators article image tend to S for some especial classes of operators S. In particular, this holds for every radial operator in the Toeplitz alg...

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Bibliographic Details
Author: Suarez, Fernando Daniel
Format: article
Status:Published version
Publication Date:2005
Country:Argentina
Institution:Consejo Nacional de Investigaciones Científicas y Técnicas
Repository:CONICET Digital (CONICET)
Language:English
OAI Identifier:oai:ri.conicet.gov.ar:11336/108528
Online Access:http://hdl.handle.net/11336/108528
Access Level:Open access
Keyword:BERGMAN SPACE
TOEPLITZ OPERATORS
BEREZIN TRANSFORMS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Description
Summary:To any bounded operator S on the Bergman space La2 we associate a sequence of linear transforms Bn(S ) ∈ L∞(D), where n ≧ 0, and prove that the Toeplitz operators article image tend to S for some especial classes of operators S. In particular, this holds for every radial operator in the Toeplitz algebra. Finally, we show that the inclusion of the Toeplitz algebra into the essential commutant of the Bergman shift is proper.