The structure of Schmidt subspaces of Hankel operators: a short proof

TL;DR

This paper provides a concise proof that Schmidt subspaces of Hankel operators are images of model spaces via isometric multipliers, linking them to nearly S*-invariant subspaces and detailing the operator's action.

Contribution

It offers a simplified proof of the structure of Schmidt subspaces of Hankel operators and introduces a formula for their action, connecting to nearly S*-invariant subspaces.

Findings

Schmidt subspaces are images of model spaces by isometric multipliers

The proof uses Hitt's theorem on nearly S*-invariant subspaces

A formula for the action of Hankel operators on these subspaces is provided

Abstract

We give a short proof of the main result of our previous paper [2]: every Schmidt subspace of a Hankel operator is the image of a model space by an isometric multiplier. This class of subspaces is closely related to nearly $S^*$-invariant subspaces, and our proof uses Hitt's theorem on the structure of such subspaces. We also give a formula for the action of a Hankel operator on its Schmidt subspace.