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Multiplication operators on Bergman spaces over polydisks associated with integer matrix

Hui Dan|Hansong Huang
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회보 (Bulletin of the KMS)|제55권 제1호|pp. 41-50

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참고문헌

키워드

von Neumann algebrajoint reducing subspaceunimodular matrix
주제분류수학

초록

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.

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.

참고문헌 (21)

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