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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, 30D55, 47A15 show english descriptions Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
${H}^p$-classes
Invariant subspaces [See also 47A46]
47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
30D55 - ${H}^p$-classes
47A15 - Invariant subspaces [See also 47A46]
 

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