文献类型：期刊文献

英文题名：Multiplication operators defined by covering maps on the Bergman space: The connection between operator theory and von Neumann algebras

作者：Guo, Kunyu[2];Huang, Hansong[1]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

年份：2011

卷号：260

期号：4

起止页码：1219

外文期刊名：JOURNAL OF FUNCTIONAL ANALYSIS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000286447500013)】；

基金：The authors thank Professor R. Douglas and Professor D. Zheng for helpful suggestions which make this paper more readable. This work is partially supported by Laboratory of Mathematics for Nonlinear Science, Fudan University, NSFC (10525106), NSFC (11001078) and NKBRPC (2006CB805905).

语种：英文

外文关键词：Holomorphic covering map; The fundamental group; Von Neumann algebra; Type II factor

摘要：In this paper, we combine methods of complex analysis, operator theory and conformal geometry to construct a class of Type II factors in the theory of von Neumann algebras, which arise essentially from holomorphic coverings of bounded planar domains. One will see how types of such von Neumann algebras are related to algebraic topology of planar domains. As a result, the paper establishes a fascinating connections to one of the long-standing problems in free group factors. An interplay of analytical, geometrical, operator and group theoretical techniques is intrinsic to the paper. (C) 2010 Elsevier Inc. All rights reserved.