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Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces

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Abstract

This paper mainly concerns a tuple of multiplication operators defined on the weighted and unweighted multi-variable Bergman spaces, their joint reducing subspaces and the von Neumann algebra generated by the orthogonal projections onto these subspaces. It is found that the weights play an important role in the structures of lattices of joint reducing subspaces and of associated von Neumann algebras. Also, a class of special weights is taken into account. Under a mild condition it is proved that if those multiplication operators are defined by the same symbols, then the corresponding von Neumann algebras are *-isomorphic to the one defined on the unweighted Bergman space.

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Author information

Authors and Affiliations

  1. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

    Hansong Huang

  2. School of Mathematics, Fudan University, Shanghai, 200433, China

    Peng Ling

Authors
  1. Hansong Huang
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  2. Peng Ling
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Correspondence to Hansong Huang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11471113, 11571064).

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Huang, H., Ling, P. Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces. Chin. Ann. Math. Ser. B 40, 187–198 (2019). https://doi.org/10.1007/s11401-019-0125-9

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  • DOI: https://doi.org/10.1007/s11401-019-0125-9

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