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.
Bibliographical noteFunding 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 ).
© 2015 Elsevier Inc.
- Class A operator
- Composition operator
- Denjoy-Wolff point
- Hyponormal operator