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

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2009-0093827 ). The first author was supported by Hankuk University of Foreign Studies Research Fund and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A2056642 ).

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

Class A operator
Composition operator
Denjoy-Wolff point
Hyponormal operator

Access to Document

10.1016/j.jmaa.2015.10.045

Cite this

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