Generalized Factorization in Hardy Spaces and the Commutant of Toeplitz Operators

Every classical inner function $\varphi$ in the unit disk gives rise to a certain factorization of functions in Hardy spaces. This factorization, which we call the generalized Riesz factorization, coincides with the classical Riesz factorization when $\varphi (z)\,=\,z$ . In this paper we prove seve...

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Bibliographic Details
Published in:Canadian journal of mathematics 2003-04, Vol.55 (2), p.379-400
Main Authors: Stessin, Michael, Zhu, Kehe
Format: Article
Language:English
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Summary:Every classical inner function $\varphi$ in the unit disk gives rise to a certain factorization of functions in Hardy spaces. This factorization, which we call the generalized Riesz factorization, coincides with the classical Riesz factorization when $\varphi (z)\,=\,z$ . In this paper we prove several results about the generalized Riesz factorization, and we apply this factorization theory to obtain a new description of the commutant of analytic Toeplitz operators with inner symbols on a Hardy space. We also discuss several related issues in the context of the Bergman space.
ISSN:0008-414X
1496-4279
DOI:10.4153/CJM-2003-017-1