Bull. Korean Math. Soc. 2018; 55(2): 507-514
Online first article September 8, 2017 Printed March 30, 2018
https://doi.org/10.4134/BKMS.b170089
Copyright © The Korean Mathematical Society.
Kei Ji Izuchi, Kou Hei Izuchi, Yuko Izuchi
Niigata University, Yamaguchi University,
Let $\{\p_n\}_{n\ge1}$ be a sequence of analytic self-maps of $\D$. It is proved that if the union set of the ranges of the composition operators $C_{\p_n}$ on the weighted Bergman spaces contains the disk algebra, then $\p_k$ is an automorphism of $\D$ for some $k\ge1$.
Keywords: composition operator, disk algebra, automorphism, weighted Bergman space, $QA$ space
MSC numbers: Primary 47B33; Secondary 46J15, 30H50
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