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Toeplitz operators on the Bergman space of the unit ball

Published online by Cambridge University Press:  17 April 2009

Roberto Raimondo
Roberto Raimondo
Affiliation:
Department of Economics, University of California at Berkeley, Evans Hall, Berkeley, CA 94720, United States of America, e-mail: [email protected]
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Abstract

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We prove that if an operator A is a finite sum of finite products of Toeplitz operators on the Bergman space of the unit ball Bn, then A is compact if and only if its Berezin transform vanishes at the boundary. For n = 1 the result was obtained by Axler and Zheng in 1997.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 273 - 285
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Axler, S. and Zheng, D., Compact operators via the Berezin transform, (preprint).Google Scholar
[2]Halmos, P.R. and Sunder, V.S., Bounded integral operators on L2 spaces (Springer-Verlag, Berlin, Heidelberg, New York, 1978).CrossRefGoogle Scholar
[3]Nowak, M., ‘Hankel operators on the Bergman space of the unit ball’, Proc. Amer, Math. Soc. 126 (1998), 2005–2015.CrossRefGoogle Scholar
[4]Rudin, W., Function theory in the unit ball of Cn (Springer-Verlag, Berlin, Heidelberg, New York, 1980).CrossRefGoogle Scholar
[5]Stroethoff, K., ‘Compact Hankel operators on the Bergman spaces of the unit ball and the polydisk in Cn’, J. Operator Theory 23 (1990), 153–170.Google Scholar