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Cowen-Thomson’s Theorem

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Multiplication Operators on the Bergman Space

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2145))

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Abstract

The root of study of reducing subspaces for multiplication operators on function spaces, as will be illustrated by subsequent chapters, lies in work on the commutants of analytic Toeplitz operators on the Hardy space \(H^{2}(\mathbb{D})\), essentially initiated by Thomson and Cowen [T1, T2, Cow1, Cow2]. In considerable detail, this chapter gives an account of Cowen-Thomson’s theorem on commutants of those operators. Also presented is Thomson’s original proof of this theorem, with some modifications. In the end of this chapter, we provide a brief review on some topics closely associated with commutants on the Hardy space, which stimulated much further work. The material of this chapter mainly comes from [T1, T2] and [Cow1].

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, China

    Kunyu Guo

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

    Hansong Huang

Authors
  1. Kunyu Guo
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  2. Hansong Huang
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Guo, K., Huang, H. (2015). Cowen-Thomson’s Theorem. In: Multiplication Operators on the Bergman Space. Lecture Notes in Mathematics, vol 2145. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46845-6_3

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