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Generalized Factorization in Hardy Spaces and the Commutant of Toeplitz Operators

Published online by Cambridge University Press:  20 November 2018

Michael Stessin  and
Kehe Zhu
Michael Stessin
Affiliation:
Department of Mathematics, SUNY, Albany, New York 12222, USA, e-mail: stessin@math.albany.edu
Kehe Zhu
Affiliation:
Department of Mathematics SUNY, Albany, New York 12222, USA, e-mail: kzhu@math.albany.edu
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Abstract

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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.

Keywords

47B3530D5547A15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 2 , 01 April 2003 , pp. 379 - 400
Copyright
Copyright © Canadian Mathematical Society 2003

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