Weighted model spaces and Schmidt subspaces of Hankel operators

Abstract

For a bounded Hankel matrix $\Gamma$, we describe the structure of the Schmidt subspaces of $\Gamma$, namely the eigenspaces of ${\Gamma }^{\ast }\Gamma$ corresponding to non zero eigenvalues. We prove that these subspaces are in correspondence with weighted model spaces in the Hardy space on the unit circle. Here we use the term "weighted model space" to describe the range of an isometric multiplier acting on a model space. Further, we obtain similar results for Hankel operators acting in the Hardy space on the real line. Finally, we give a streamlined proof of the Adamyan-Arov-Krein theorem using the language of weighted model spaces.

Final version, to appear in Journal of the London Mathematical Society

References in corpus (1)

• Inverse spectral theory for a class of non-compact Hankel operators

Cited by in corpus (3)

• Inverse spectral theory for a class of non-compact Hankel operators
• Turbulent cascades for a family of damped Szegö equations
• The structure of Schmidt subspaces of Hankel operators: a short proof