Composition Operators with Linear Fractional Symbols on Vector-Valued Bergman Spaces

Letψ and ψ be linear fractional self-maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation Cψ with another one’s adjoint Cψ^* on the vector-valued Bergman space B1(X) for forms CψCψ^*...

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Bibliographic Details
Published in:Wuhan University journal of natural sciences 2003-09, Vol.8 (3A), p.759-764
Main Author: WangMao-fa UuPei-de ZhouShao-bo
Format: Article
Language:English
Subjects:
Banach空间
Composition
Hilbert space
Operators
合成算子
向量值Bergman函数
弱紧性
角微商
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Summary:Letψ and ψ be linear fractional self-maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation Cψ with another one’s adjoint Cψ^* on the vector-valued Bergman space B1(X) for forms CψCψ^* and Cψ^* Cψ.
ISSN:1007-1202
1993-4998
DOI:10.1007/BF02900811