# MULTIPLICATION OPERATORS ON BERGMAN SPACES OVER POLYDISKS ASSOCIATED WITH INTEGER MATRIX

• Dan, Hui (School of Mathematical Sciences Fudan University) ;
• Huang, Hansong (Department of Mathematics East China University of Science and Technology)
• Accepted : 2017.06.14
• Published : 2018.01.31

#### Abstract

This paper mainly considers a tuple of multiplication operators on Bergman spaces over polydisks which essentially arise from a matrix, their joint reducing subspaces and associated von Neumann algebras. It is shown that there is an interesting link of the non-triviality for such von Neumann algebras with the determinant of the matrix. A complete characterization of their abelian property is given under a more general setting.

#### Acknowledgement

Supported by : NSFC, CSC, Shanghai Center for Mathematical Sciences

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