Science China Mathematics

, Volume 58, Issue 10, pp 1–14 | Cite as

Reducing subspaces of multiplication operators with the symbol αzk + βwl on \(L_a^2 (\mathbb{D}^2 )\)

Articles

Abstract

Multiplication operators defined on function spaces have been receiving enormous attention from both operator-theoretic and function-theoretic experts. One of the problems is to study reducing subspaces of them. The one-variable case has obtained fruitful remarkable results. However, little has been done in the multi-variable case. Under the setting of the Bergman space \(L_a^2 (\mathbb{D}^2 )\), this paper addresses those multiplication operators Mp defined by special polynomials p, where p(z,w) = αzk +βwl, α, β ∈ ℂ. Those reducing subspaces of Mp are completely determined.

Keywords

von Neumann algebra reducing subspaces multiplication operators 

MSC(2010)

47C15 47B32 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiChina
  2. 2.Department of MathematicsEast China University of Science and TechnologyShanghaiChina

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