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Compact operators on the Bergman space of multiply-connected domains

Author(s): Roberto Raimondo
Journal: Proc. Amer. Math. Soc. 129 (2001), 739-747.
MSC (2000): Primary 47B35
Posted: September 19, 2000
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Abstract:

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
Email: raimondo@econ.berkeley.edu

DOI: 10.1090/S0002-9939-00-05718-X
PII: S 0002-9939(00)05718-X
Received by editor(s): May 4, 1999
Posted: September 19, 2000
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2000, American Mathematical Society

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