Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces

作     者：Hansong HUANG Peng LING 

作者机构：Department of Mathematics East China University of Science and Technology School of Mathematics Fudan University 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2019年第40卷第2期

页      面：187-198页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.11471113 11571064) 

主　　题：Joint reducing subspaces Von Neumann algebras Weighted Bergman spaces 

摘      要：This paper mainly concerns a tuple of multiplication operators defined on the weighted and unweighted multi-variable Bergman spaces, their joint reducing subspaces and the von Neumann algebra generated by the orthogonal projections onto these subspaces. It is found that the weights play an important role in the structures of lattices of joint reducing subspaces and of associated von Neumann algebras. Also, a class of special weights is taken into account. Under a mild condition it is proved that if those multiplication operators are defined by the same symbols, then the corresponding von Neumann algebras are *-isomorphic to the one defined on the unweighted Bergman space.