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2015 | OriginalPaper | Chapter

3. Cowen-Thomson’s Theorem

Authors : Kunyu Guo, Hansong Huang

Published in: Multiplication Operators on the Bergman Space

Publisher: Springer Berlin Heidelberg

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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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previous chapter Some Preliminaries

next chapter Reducing Subspaces Associated with Finite Blaschke Products

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Title: Cowen-Thomson’s Theorem
Authors: Kunyu Guo
Hansong Huang
Publisher: Springer Berlin Heidelberg
Book: Multiplication Operators on the Bergman Space
Print ISBN: 978-3-662-46844-9

Electronic ISBN: 978-3-662-46845-6

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-662-46845-6_3

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