| 张芬,周泽华.单位球中解析函数Hilbert空间上的加权复合算子的伴随及其应用[J].数学年刊A辑,2009,30(2):153~160 |
| 单位球中解析函数Hilbert空间上的加权复合算子的伴随及其应用 |
| Adjoints of Weighted Composition Operators on the Hilbert Spaces of Analytic Functions in the Unit Ball and Its Applications |
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| DOI： |
| 中文关键词: 加权复合算子 自伴性 对偶算子 |
| 英文关键词:Weighted composition operator, Self-adjointness, Adjoint operator |
| 基金项目:国家自然科学基金 |
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| 中文摘要: |
| 主要给出了具有再生核的解析函数Hilbert空间中由任意$\varphi$ 及$\psi$所导出的加权复合算子
的对偶算子的一般公式.在此基础上,得到了由一些特殊函数所导出的加权复合算子$C_{\varphi ,\psi }$的
对偶算子的更优美结果.最后还给出了加权Bergman空间中$C_{\varphi ,\psi }$自伴的充要条件. |
| 英文摘要: |
| This paper presents a general formula for the adjoint of a weighted composition operator
available for all admissible $\varphi$ and $\psi$ in any Hilbert
spaces of analytic functions with reproducing kernels. As the base
of this, some improved explicit expressions for the adjoint of
$C_{\varphi ,\psi }$ induced by specific $\varphi$ and $\psi$ are
obtained, and the characterization for $C_{\varphi ,\psi }$ to be
self-adjoint on the weighted Bergman space is also given. |
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