Hankel Operators over Compact Abelian Groups

TL;DR

This paper extends the theory of Hankel operators to linearly ordered abelian groups, providing criteria for boundedness and compactness, and exploring their properties and applications in Toeplitz operator theory.

Contribution

It introduces new variants of Hankel operators on linearly ordered abelian groups and establishes criteria for their boundedness, compactness, and non-Fredholmness, with applications to Toeplitz operators.

Findings

Criteria for boundedness and compactness are established.

Non-Fredholmness of generalized Hankel operators is proved.

Applications to Toeplitz operators on groups are provided.

Abstract

Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean oscillation, the nonfredholmness of generalized Hankel operators is proved. Some applications to the theory of Toeplitz operators on groups are given.