On compact Hankel operators over compact Abelian groups

TL;DR

This paper extends classical theorems on Hankel operators to the setting of compact Abelian groups with linearly ordered duals, providing new structural insights and applications.

Contribution

It generalizes key classical theorems for Hankel operators to the context of compact Abelian groups with ordered duals, including invariant subspace results.

Findings

Generalized Kronecker, Hartman, Peller, and Adamyan-Arov-Krein theorems

Described structure of compact Hankel operators over G

Extended Burling's invariant subspace theorem

Abstract

We consider compact and connected Abelian group $G$ with a linearly ordered dual. Based on the description of the structure of compact Hankel operators over $G$, generalizations of the classical Kronecker, Hartman, Peller and Adamyan-Arov-Krein theorems are obtained. A generalization of Burling's invariant subspace theorem is also established. Applications are given to Hankel operators over discrete groups