Abstract
Let φ and ϕ be linear fractional self-maps of the unit diskD andX a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operationC φ with another one’s adjointC *ρ on the vector-valued Bergman spaceB 1 (X) for formsC φC *φ andC *φ Cφ.
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Foundation item: Supported by the National Natural Science Foundation of China (19771063)
Biography: Wang Mao fa(1971-), male, Lecturer, research direetion: functional analysis.
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Mao-fa, W., Pei-de, L. & Shao-bo, Z. Composition operators with linear fractional symbols on vector-valued Bergman spaces. Wuhan Univ. J. of Nat. Sci. 8, 759–764 (2003). https://doi.org/10.1007/BF02900811
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DOI: https://doi.org/10.1007/BF02900811
Key words
- vector-valued Bergman space
- composition operator
- linear fractional map
- angular derivative
- weak compactness