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Hankel operators on the Bergman space of the unit ball

Author(s): Maria Nowak
Journal: Proc. Amer. Math. Soc. 126 (1998), 2005-2012.
MSC (1991): Primary 30H05, 47B38
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Abstract: We characterize the bounded holomorphic functions $ f, g $ in the unit ball of $ \mathbb{C}^{n} $ for which the operator $ H^{*}_{\bar g} H_{\bar f} $ is compact. For $ n=1 $ the result was obtained by Axler and Gorkin in 1988 and by Zheng in 1989.

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Additional Information:

Maria Nowak
Affiliation: Instytut Matematyki UMCS , pl. Marii Curie-Sklodowskiej 1,20-031 Lublin, Poland
Email: nowakm@golem.umcs.lublin.pl

DOI: 10.1090/S0002-9939-98-04252-X
PII: S 0002-9939(98)04252-X
Received by editor(s): December 6, 1995
Received by editor(s) in revised form: December 10, 1996
Additional Notes: This work was supported in part by KBN grant No. 2 PO3A- 002-08.
Communicated by: Theodore W. Gamelin
Copyright of article: Copyright 1998, American Mathematical Society

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