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Multiplication Operators Defined by a Class of Polynomials on \({L_a^2(\mathbb{D}^2)}\)

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Abstract

In this paper, we consider those multiplication operators M p on \({L_a^2(\mathbb{D}^2)}\) defined by a class of polynomials p. Also, this paper consider the reducing subspaces of M p , the von Neumann algebra \({ \mathcal{W}^*(p)}\) generated by M p , and its commutant \({\mathcal{V}^*(p) = \mathcal{W}^*(p)'.}\) The structure of \({\mathcal{V}^*(p)}\) is completely determined, along with those reducing subspaces of M p .

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Authors and Affiliations

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

    Hui Dan & Hansong Huang

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  1. Hui Dan
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  2. Hansong Huang
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Correspondence to Hansong Huang.

Additional information

This work was partially supported by NSFC(11001078) and CSC(201406745016).

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Dan, H., Huang, H. Multiplication Operators Defined by a Class of Polynomials on \({L_a^2(\mathbb{D}^2)}\) . Integr. Equ. Oper. Theory 80, 581–601 (2014). https://doi.org/10.1007/s00020-014-2176-3

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  • DOI: https://doi.org/10.1007/s00020-014-2176-3

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