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COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON BERGMAN SPACES IN THE BALL

Part of: Holomorphic functions of several complex variables

Published online by Cambridge University Press:  14 March 2011

XIANG DONG YANG  and
LE HAI KHOI
XIANG DONG YANG*
Affiliation:
Department of Mathematics, Kunming University of Science and Technology, 650093 Kunming, Yunnan Province, PR China (email: [email protected])
LE HAI KHOI
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We obtain necessary and sufficient conditions for the compactness of differences of composition operators acting on the weighted Bergman spaces in the unit ball. A representation of a composition operator as a finite sum of composition operators modulo compact operators is also studied.

Keywords

Bergman spacecomposition operatorcompact difference

MSC classification

Secondary: 32A36: Bergman spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 3 , December 2010 , pp. 407 - 418
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The first author is supported by the Natural Science Foundation of Yunnan Province in China (Grant No. 2009ZC013X) and the Basic Research Foundation of the Education Bureau of Yunnan Province in China (Grant No. 09Y0079).

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