文献类型：期刊文献

中文题名：Reducing subspaces of multiplication operators with the symbol αz^k+ βw^l on L_a^2(D^2)

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

作者：WANG XuDi[1];DAN Hui[2];HUANG HanSong[2]

机构：[1]School of Mathematical Sciences, Fudan University;[2]Department of Mathematics, East China University of Science and Technology

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：中国科学：数学（英文版）

收录：Scopus;CSCD:【CSCD2015_2016】；PubMed;

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

语种：英文

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

外文关键词：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

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 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.