Bulletin of the
Korean Mathematical Society BKMS

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