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

作　　者：张芬[1] 周泽华[1] 

机构地区：[1]天津大学数学系,天津300072

出　　处：《数学年刊（A辑）》2009年第2期153-160,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10671141;No.10371091)资助的项目.

摘　　要：主要给出了具有再生核的解析函数Hilbert空间中由任意φ及Ψ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_(φ,Ψ)的对偶算子的更优美结果.最后还给出了加权Bergman空间中C_(φ,Ψ)自伴的充要条件.This paper presents a general formula for the adjoint of a weighted composition operator available for all admissible 99 and ψ in any Hilbert spaces of analytic functions with reproducing kernels. As the base of this, some improved explicit expressions for the adjoint of Cφ,ψ induced by specific φ and ψ are obtained, and the characterization for Cφ,ψ to be self-adjoint on the weighted Bergman space is also given.

关 键 词：加权复合算子 自伴性 对偶算子 

分 类 号：O174.56[理学—数学]