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http://dx.doi.org/10.4134/BKMS.b160833

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.1, 2018 , pp. 41-50 More about this Journal
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;
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Times Cited By KSCI : 1  (Citation Analysis)
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