文献类型：期刊文献

中文题名：Von Neumann algebras generated by multiplication operators on the weighted Bergman space:A function-theory view into operator theory

英文题名：von Neumann algebras generated by multiplication operators on the weighted Bergman space: a function-theory view into operator theory

作者：Huang HanSong

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2013

卷号：56

期号：4

起止页码：811

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:000316746800012)】；PubMed;

基金：This work was supported by National Natural Science Foundation of China (Grant No. 11001078), Shanghai Municipal Education Commission and Shanghai Education Development Foundation (Grant No. 11CG30).

语种：英文

中文关键词：weighted Bergman space; holomorphic covering map; the fundamental group; yon Neumann algebra; Type Ⅱ factor

外文关键词：weighted Bergman space; holomorphic covering map; the fundamental group; von Neumann algebra; Type II factor

摘要：Recently,a class of Type Ⅱ factors has been constructed,arising from holomorphic coverings of bounded planar domains.Those operators in Type Ⅱ factors act on the Bergman space.In this paper,we develop new techniques to generalize those results to the case of the weighted Bergman spaces.In addition,a class of group-like von Neumann algebras are constructed,which are shown to be-isomorphic to the group von Neumann algebras.
Recently, a class of Type II factors has been constructed, arising from holomorphic coverings of bounded planar domains. Those operators in Type II factors act on the Bergman space. In this paper, we develop new techniques to generalize those results to the case of the weighted Bergman spaces. In addition, a class of group-like von Neumann algebras are constructed, which are shown to be *-isomorphic to the group von Neumann algebras.