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SPECTRA OF LINEAR FRACTIONAL COMPOSITION OPERATORS ON THE GROWTH SPACE AND BLOCH SPACE OF THE UPPER HALF-PLANE

Part of: Special classes of linear operators

Published online by Cambridge University Press:  29 October 2018

SHI-AN HAN  and
ZE-HUA ZHOU Open the ORCID record for ZE-HUA ZHOU [Opens in a new window]
SHI-AN HAN
Affiliation:
School of Mathematics, Tianjin University, Tianjin 300354, PR China email hsatju@163.com
ZE-HUA ZHOU*
Affiliation:
School of Mathematics, Tianjin University, Tianjin 300354, PR China email zehuazhoumath@aliyun.com, zhzhou@tju.edu.cn
*
✉zehuazhoumath@aliyun.com
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Abstract

In this article, we provide a complete description of the spectra of linear fractional composition operators acting on the growth space and Bloch space over the upper half-plane. In addition, we also prove that the norm, essential norm, spectral radius and essential spectral radius of a composition operator acting on the growth space are all equal.

Keywords

composition operatorupper half-planespectragrowth spaceBloch space

MSC classification

Primary: 47B33: Composition operators
Secondary: 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47B38: Operators on function spaces (general)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 107 , Issue 2 , October 2019 , pp. 199 - 214
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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Footnotes

The work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11771323; 11371276).

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