Multiplication operators on Bergman spaces over polydisks associated with integer matrix
Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 41-50
Published online January 31, 2018
Hui Dan, Hansong Huang
Fudan University, East China University of Science and Technology
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.
Keywords : von Neumann algebra, joint reducing subspace, unimodular matrix
MSC numbers : 47A13, 47C15
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