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Compact operators on the Bergman space of multiply-connected domains

Author: Roberto Raimondo
Journal: Proc. Amer. Math. Soc. 129 (2001), 739-747
MSC (2000): Primary 47B35
Published electronically: September 19, 2000
MathSciNet review: 1801999
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Abstract | References | Similar Articles | Additional Information


If $\Omega $ is a smoothly bounded multiply-connected domain in the complex plane and $A=\sum_{j=1}^m\prod_{k=1}^{m_j}T_{\varphi _{j,k}},$where $\varphi _{j,k}\in L^\infty ({\Omega },d{\nu }),$we show that $A$ is compact if and only if its Berezin transform vanishes at the boundary.

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Additional Information

Roberto Raimondo
Affiliation: Department of Economics, University of California at Berkeley, Evans Hall, Berkeley, California 94720

Received by editor(s): May 4, 1999
Published electronically: September 19, 2000
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2000 American Mathematical Society