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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 $k\ge1$.
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참고문헌 (10)
참고문헌 신청
C. Cowen / 1995 / Composition Operators on Spaces of Analytic Functions / CRC Press
J. Garnett / 1981 / Bounded Analytic Functions / Academic Press
H. Hedenmalm / 2000 / Theory of Bergman Spaces / Springer
K. Hoffman / 1962 / Banach Spaces of Analytic Functions / Prentice Hall
K. J. Izuchi / 2015 / Weighted composition operators whose ranges contain the disk algebra / Complex Var. Elliptic Equ. 60(7):938~944
J. Garnett / 1981 / Bounded Analytic Functions / Academic Press
H. Hedenmalm / 2000 / Theory of Bergman Spaces / Springer
K. Hoffman / 1962 / Banach Spaces of Analytic Functions / Prentice Hall
K. J. Izuchi / 2015 / Weighted composition operators whose ranges contain the disk algebra / Complex Var. Elliptic Equ. 60(7):938~944
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