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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

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