文献类型：期刊文献

中文题名：Reducing subspaces of multiplication operators with the symbol αzk+ βwlon L2a(D2)

英文题名：Reducing subspaces of multiplication operators with the symbol αzk + βwl on La2(D2)

作者：Wang XuDi[1];Dan Hui[2];Huang HanSong[2]

机构：[1]Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China;[2]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2015

卷号：58

期号：10

起止页码：2167

中文期刊名：Science China Mathematics

外文期刊名：SCIENCE CHINA-MATHEMATICS

收录：;Scopus;WOS:【SCI-EXPANDED(收录号:WOS:000361765300010)】；CSCD:【CSCD2015_2016】；PubMed;

基金：This work was supported by National Natural Science Foundation of China (Grant No. 11471113).

语种：英文

中文关键词：算子空间;乘法算子;算子多项式;函数空间;多变量;定义;MP;极大

外文关键词：von Neumann algebra; reducing subspaces; multiplication operators

摘要：Multiplication operators defined on function spaces have been receiving enormous attention from both operator-theoretic and function-theoretic experts. One of the problems is to study reducing subspaces of them. The one-variable case has obtained fruitful remarkable results. However, little has been done in the multi-variable case. Under the setting of the Bergman space L2a(D2), this paper addresses those multiplication operators Mp defined by special polynomials p, where p(z, w) = αzk+ βwl, α, β∈ C. Those reducing subspaces of Mp are completely determined.
Multiplication operators defined on function spaces have been receiving enormous attention from both operator-theoretic and function-theoretic experts. One of the problems is to study reducing subspaces of them. The one-variable case has obtained fruitful remarkable results. However, little has been done in the multi-variable case. Under the setting of the Bergman space L-a(2)(D-2), this paper addresses those multiplication operators M-p defined by special polynomials p, where p(z, w) = alpha z(k) + beta w(l), alpha, beta is an element of C. Those reducing subspaces of M-p are completely determined.