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We study m-Berezin transforms of bounded operators on the Bergman space over a bounded symmetric domain, $$\Omega $$Ω. We use the m-Berezin transform to establish some results on norm approximation… Click to show full abstract
We study m-Berezin transforms of bounded operators on the Bergman space over a bounded symmetric domain, $$\Omega $$Ω. 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.
Journal Title: Complex Analysis and Operator Theory
Year Published: 2017
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