Multiplication operators defined by a class of polynomials on L_a²(D²)

2014/04/22 by Dan, Hui, Huang, Hansong
#47B32 #47C15 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1404.5414

Abstract

In this paper, we consider those multiplication operators M_p on the Bergman space L_a²(D²) over the bidisk, defined by a class of polynomials p. Also, this paper consider the reducing subspaces of M_p, the von Neumann algebra W^*(p) generated by M_p, and its commutant V^*(p)=W^*(p)'. The structure of V^*(p) is completely determined, along with those reducing subspaces of M_p.

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