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# Generalized Factorization in Hardy Spaces and the Commutant of Toeplitz Operators

Published:2003-04-01
Printed: Apr 2003
• Michael Stessin
• Kehe Zhu
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## Abstract

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.
 MSC Classifications: 47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15] 30D55 - ${H}^p$-classes47A15 - Invariant subspaces [See also 47A46]