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COMPOSITION OPERATORS BELONGING TO SCHATTEN CLASS 𝒮p

Part of: Special classes of linear operators Holomorphic functions of several complex variables

Published online by Cambridge University Press:  17 March 2010

CHENG YUAN  and
ZE-HUA ZHOU
CHENG YUAN
Affiliation:
School of Science, Tianjin University of Technology and Education, Tianjin, PR China (email: yuancheng1984@163.com)
ZE-HUA ZHOU*
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China (email: zehuazhou2003@yahoo.com.cn)
*
✉For correspondence; e-mail: zehuazhou2003@yahoo.com.cn
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Abstract

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We investigate the composition operators Cφ acting on the Bergman space of the unit disc D, where φ is a holomorphic self-map of D. Some new conditions for Cφ to belong to the Schatten class 𝒮p are obtained. We also construct a compact composition operator which does not belong to any Schatten class.

Keywords

Bergman spacescomposition operatorsSchatten class

MSC classification

Secondary: 47B38: Operators on function spaces (general) 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 3 , June 2010 , pp. 465 - 472
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

Supported in part by the National Natural Science Foundation of China (grants 10971153, 10671141).

References

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