# Fredholm and spectral properties of Toeplitz operators on $H^p$ spaces over ordered groups

## TL;DR

This paper extends classical results on Toeplitz operators to spaces over ordered groups, establishing Fredholm properties and spectral theory implications, with applications and explicit index computations.

## Contribution

It generalizes the Gohberg-Krein theorem for Toeplitz operators on $H^p(G)$ spaces over ordered groups, including spectral analysis and index calculations.

## Key findings

- Proved the Fredholm property for Toeplitz operators with continuous symbols.
- Established a generalized Gohberg-Krein index theorem.
- Provided explicit examples of index computation.

## Abstract

Toeplitz operators on spaces $H^p(G)\ (1< p<\infty)$ associated with compact connected Abelian group $G$ with ordered dual are considered and the generalization of the classical Gohberg-Krein theorem on the Fredholm index of such operators with continuous symbols is proved. Applications to spectral theory of Toeplitz operators are given and examples of evident computation of index have been considered.