Weighted model spaces and Schmidt subspaces of Hankel operators

TL;DR

This paper characterizes the structure of Schmidt subspaces of Hankel operators using weighted model spaces in Hardy spaces, providing new insights and a streamlined proof of the Adamyan-Arov-Krein theorem.

Contribution

It establishes a correspondence between Schmidt subspaces of Hankel operators and weighted model spaces, extending results to Hardy spaces on the real line, and offers a simplified proof of a key theorem.

Findings

Schmidt subspaces correspond to weighted model spaces

Results apply to Hardy spaces on the real line

Provides a streamlined proof of the Adamyan-Arov-Krein theorem

Abstract

For a bounded Hankel matrix $\Gamma$, we describe the structure of the Schmidt subspaces of $\Gamma$, namely the eigenspaces of $\Gamma^* \Gamma$ 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.