Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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WEIGHTED COMPOSITION OPERATORS WHOSE RANGES CONTAIN THE DISK ALGEBRA II

  • Received : 2017.02.01
  • Accepted : 2017.06.08
  • Published : 2018.03.31
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Abstract

Let $\{{\varphi}_n\}_{n{\geq}1}$ be a sequence of analytic self-maps of ${\mathbb{D}}$. It is proved that if the union set of the ranges of the composition operators $C_{{\varphi}_n}$ on the weighted Bergman spaces contains the disk algebra, then ${\varphi}_k$ is an automorphism of ${\mathbb{D}}$ for some $k{\geq}1$.

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References

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