Class A composition operators on H2

Sungeun Jung; Eungil Ko

doi:10.1016/j.jmaa.2015.10.045

Class A composition operators on H²

Sungeun Jung, Eungil Ko

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we study class A composition operators C_φ on the Hardy space H². We show that if C_φ belongs to class A, then 0 is a fixed point of the symbol φ. As a corollary, we obtain that every invertible class A composition operator is unitary. Moreover, we examine spectral properties and the commutants of class A composition operators. We also prove that if φ is a linear fractional self-map of D into itself, then C_φ belongs to class A if and only if it is subnormal. Finally, we provide some conditions under which Cφ* belongs to class A.

Original language	English
Pages (from-to)	461-476
Number of pages	16
Journal	Journal of Mathematical Analysis and Applications
Volume	435
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2015.10.045
State	Published - 1 Mar 2016

Keywords

Class A operator
Composition operator
Denjoy-Wolff point
Hyponormal operator

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10.1016/j.jmaa.2015.10.045

Cite this

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abstract = "In this paper, we study class A composition operators Cφ on the Hardy space H2. We show that if Cφ belongs to class A, then 0 is a fixed point of the symbol φ. As a corollary, we obtain that every invertible class A composition operator is unitary. Moreover, we examine spectral properties and the commutants of class A composition operators. We also prove that if φ is a linear fractional self-map of D into itself, then Cφ belongs to class A if and only if it is subnormal. Finally, we provide some conditions under which Cφ* belongs to class A.",

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AB - In this paper, we study class A composition operators Cφ on the Hardy space H2. We show that if Cφ belongs to class A, then 0 is a fixed point of the symbol φ. As a corollary, we obtain that every invertible class A composition operator is unitary. Moreover, we examine spectral properties and the commutants of class A composition operators. We also prove that if φ is a linear fractional self-map of D into itself, then Cφ belongs to class A if and only if it is subnormal. Finally, we provide some conditions under which Cφ* belongs to class A.

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KW - Composition operator

KW - Denjoy-Wolff point

KW - Hyponormal operator

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