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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Compact composition operators on BMOA and the Bloch space


Authors: Hasi Wulan, Dechao Zheng and Kehe Zhu
Journal: Proc. Amer. Math. Soc. 137 (2009), 3861-3868
MSC (2000): Primary 47B38; Secondary 30D50
Published electronically: June 15, 2009
MathSciNet review: 2529895
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Abstract: We give a new and simple compactness criterion for composition operators $ C_\varphi$ on BMOA and the Bloch space in terms of the norms of $ \varphi^n$ in the respective spaces.


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Additional Information

Hasi Wulan
Affiliation: Department of Mathematics, Shantou University, Guangdong, People’s Republic of China
Email: wulan@stu.edu.cn

Dechao Zheng
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37235
Email: dechao.zheng@vanderbilt.edu

Kehe Zhu
Affiliation: Department of Mathematics, State University of New York, Albany, New York 12222
Email: kzhu@math.albany.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09961-4
PII: S 0002-9939(09)09961-4
Received by editor(s): January 16, 2009
Received by editor(s) in revised form: March 8, 2009
Published electronically: June 15, 2009
Additional Notes: The first and third authors were supported by the China National Natural Science Foundation.
The second and third authors were supported by the U.S. National Science Foundation.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society