m-Berezin Transform and Approximation of Operators on the Bergman Space Over Bounded Symmetric Domains
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We study m-Berezin transforms of bounded operators on the Bergman space over a bounded symmetric domain, \(\Omega \). We use the m-Berezin transform to establish some results on norm approximation of bounded linear operators acting on the Bergman space by means of Toeplitz operators. We also use the m-Berezin transform to study compactness of bounded operators. In particular we show that a radial operator in the Toeplitz algebra is compact if and only if its Berezin transform vanishes on the boundary of the bounded symmetric domain.
KeywordsBounded symmetric domain m-Berezin transform Toeplitz operator
The author is grateful to Professor Wolfram Bauer for his useful comments and discussions and to Professor David Békollé for accepting to read through the manuscript and making some corrections.
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