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December, 2006 $m$-Berezin transform and compact operators
Kyesook Nam , Dechao Zheng , Changyong Zhong
Rev. Mat. Iberoamericana 22(3): 867-892 (December, 2006).


$m$-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the $m$-Berezin transform as a linear operator from the space of bounded operators to $L^{\infty}$ is found. We show that the $m$-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the $m$-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary of the unit ball.


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Kyesook Nam . Dechao Zheng . Changyong Zhong . "$m$-Berezin transform and compact operators." Rev. Mat. Iberoamericana 22 (3) 867 - 892, December, 2006.


Published: December, 2006
First available in Project Euclid: 22 January 2007

zbMATH: 1125.47020
MathSciNet: MR2320405

Primary: 47B35 , 47B38

Keywords: $m$-Berezin transforms , Toeplitz operators

Rights: Copyright © 2006 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.22 • No. 3 • December, 2006
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