Multiplication operators on Bergman spaces over polydisks associated with integer matrix

Hui Dan; Hansong Huang

doi:10.4134/BKMS.b160833

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2018; 55(1): 41-50

Online first article December 28, 2017 Printed January 31, 2018

https://doi.org/10.4134/BKMS.b160833

Multiplication operators on Bergman spaces over polydisks associated with integer matrix

Hui Dan, Hansong Huang

Fudan University, East China University of Science and Technology

Abstract

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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