文献类型：期刊文献

中文题名：Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces

英文题名：Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces

作者：Hansong HUANG[1];Peng LING[2]

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

年份：2019

卷号：40

期号：2

起止页码：187

中文期刊名：Chinese Annals of Mathematics,Series B

外文期刊名：数学年刊（B辑英文版）

收录：CSTPCD;;Scopus;CSCD:【CSCD2019_2020】；

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

语种：英文

中文关键词：Joint;reducing;subspaces;Von;Neumann;algebras;Weighted;Bergman;spaces

外文关键词：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.
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.