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DIFFERENCES OF COMPOSITION OPERATORS ON THE BLOCH SPACE IN THE POLYDISC

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

Published online by Cambridge University Press:  17 April 2009

ZHONG-SHAN FANG  and
ZE-HUA ZHOU
ZHONG-SHAN FANG
Affiliation:
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, PR China (email: fangzhongshan@yahoo.com.cn)
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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Let φ and ψ be holomorphic self-maps of the unit polydisc Un in the n-dimensional complex space, and denote by Cφ and Cψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators Cφ−Cψ from Bloch space to bounded holomorphic function space in the unit polydisc. The compactness of the difference is also characterized.

Keywords

essential normcompact differencecomposition operatorBloch spacepolydiscs

MSC classification

Secondary: 47B38: Operators on function spaces (general) 32A26: Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels) 32A30: Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) 32A38: Algebras of holomorphic functions 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions 47B33: Composition operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 3 , June 2009 , pp. 465 - 471
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The second author was supported in part by the National Natural Science Foundation of China (Grant Nos. 10671141, 10371091).

References

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