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

作者：Guo, Kunyu; Huang, Hansong^*

来源：Journal of Functional Analysis, 2011, 260(4): 1219-1255.

DOI：10.1016/j.jfa.2010.11.002

• Holomorphic covering map
• The fundamental group
• Von Neumann algebra
• Type II factor

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.

• 出版日期2011-2-28
• 单位复旦大学; 华东理工大学