Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces |
| |
Authors: | Huang Hansong Ling Peng |
| |
Affiliation: | Department of Mathematics, East China University of Scienceand Technology, Shanghai 200237, China. and School of Mathematics, Fudan University, Shanghai 200433, China. |
| |
Abstract: | This paper mainly concerns a tuple of multiplication operatorsdefined on the weighted and unweighted multi-variable Bergmanspaces, their joint reducing subspaces and the von Neumann algebragenerated by the orthogonal projections onto these subspaces. It isfound that the weights play an important role in the structures oflattices of joint reducing subspaces and of associated von Neumannalgebras. Also, a class of special weights is taken into account.Under a mild condition it is proved that if those multiplicationoperators are defined by the same symbols, then the correspondingvon Neumann algebras are $*$-isomorphic to the one defined on theunweighted Bergman space. |
| |
Keywords: | Joint reducing subspaces Von Neumann algebras Weighted Bergmanspaces |
本文献已被 CNKI SpringerLink 等数据库收录! |
| 点击此处可从《数学年刊B辑(英文版)》浏览原始摘要信息 |
|
点击此处可从《数学年刊B辑(英文版)》下载全文 |
|