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Daniel Suárez

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

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.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2005, 04/2005
Pages: 175 - 192

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