单位双圆盘Hardy空间上乘法算子的一些性质  

Some Properties of Multiplication Operators on the Hardy Space over the Bidisk

作　　者：韩凯凯 王茂发[2] HAN Kaikai;WANG Maofa(School of Mathematics and Statistics,Hebei University of Economics and Business,Shijiazhuang 050061,Hebei,China;School of Mathematics and Statistics,Wuhan University,Wuhan 430072,Hubei,China)

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061 [2]武汉大学数学与统计学院,湖北武汉430072

出　　处：《武汉大学学报（理学版）》2021年第3期277-280,共4页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金(11771340)。

摘　　要：设φ是单位双圆盘上的解析函数,研究了单位双圆盘Hardy空间上乘法算子Mφ的一些性质。具体地,给出了单位双圆盘Hardy空间上有界线性算子是乘法算子的一种刻画。证明了有界乘法算子Mφ的本性范数等于φ的上确界范数,揭示了单位双圆盘Hardy空间上没有非平凡的紧乘法算子。给出了乘法算子是满射的充分必要条件,描述了乘法算子的谱。利用Poisson积分的方法刻画了闭值域的乘法算子。This paper considers some properties of multiplication operators Mφon the Hardy space over the bidisk,whereφis an analytic function on the bidisk.Concretely,we gave a characterization when a bounded linear operator on the Hardy space over the bidisk is a multiplication operator.The essential norm of a bounded multiplication operator Mφwas proved to be equal to the supremum norm ofφ,which reveals that there exists no non-trivial compact multiplication operators on the Hardy space over the bidisk.Moreover,we gave a sufficient and necessary condition when a multiplication operator was surjective,and described the spectra of multiplication operators.Finally,by using Poisson integral,we characterized multiplication operators with closed range.

关 键 词：单位双圆盘Hardy空间 乘法算子 本性范数 谱 

分 类 号：O177[理学—数学]