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ESSENTIAL COMMUTATIVITY OF SOME INTEGRAL AND COMPOSITION OPERATORS

Part of: Integral operators Linear function spaces and their duals Special classes of linear operators Spaces and algebras of analytic functions

Published online by Cambridge University Press:  20 October 2011

ZE-HUA ZHOU ,
LIANG ZHANG  and
HONG-GANG ZENG
ZE-HUA ZHOU*
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China (email: zehuazhou2003@yahoo.com.cn)
LIANG ZHANG
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China (email: 168zhangliang2011@163.com)
HONG-GANG ZENG
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China (email: zhgng@tju.edu.cn)
*
✉For correspondence; e-mail: zehuazhou2003@yahoo.com.cn
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Abstract

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In general, multiplication of operators is not essentially commutative in an algebra generated by integral-type operators and composition operators. In this paper, we characterize the essential commutativity of the integral operators and composition operators from a mixed-norm space to a Bloch-type space, and give a complete description of the universal set of integral operators. Corresponding results for boundedness and compactness are also obtained.

Keywords

essential commutativityintegral-type operatorscomposition operators

MSC classification

Secondary: 47B38: Operators on function spaces (general) 45P05: Integral operators 46E15: Banach spaces of continuous, differentiable or analytic functions 30H30: Bloch spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 1 , February 2012 , pp. 143 - 153
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The first author was supported in part by the National Natural Science Foundation of China (Grant Nos. 10971153, 10671141).

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