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

Daniel Suárez

doi:10.1515/crll.2005.2005.581.175

Published by De Gruyter July 27, 2005

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

Daniel Suárez

From the journal Journal für die reine und angewandte Mathematik

https://doi.org/10.1515/crll.2005.2005.581.175

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Abstract

To any bounded operator S on the Bergman space L_a² we associate a sequence of linear transforms B_n(S ) ∈ L^∞(D), where n ≧ 0, and prove that the Toeplitz operators

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.

Published Online: 2005-07-27

Published in Print: 2005-04-26

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

Abstract

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