Quasi-Hermitian pair and co-amenability

TL;DR

This paper extends the concept of quasi-Hermitian groups to pairs of discrete groups and their subgroups, establishing that such pairs are amenable in the sense of Eymard, thus linking algebraic properties to amenability.

Contribution

It introduces the notion of quasi-Hermitian pairs of groups and proves their amenability, providing a new perspective on the relationship between algebraic structures and harmonic analysis.

Findings

Quasi-Hermitian pairs are shown to be amenable.

The paper generalizes the concept of quasi-Hermitian groups to pairs of groups.

Establishes a connection between quasi-Hermitian properties and Eymard's amenability.

Abstract

We adapt the notion of quasi-Hermition group to the pairs $(G,H)$ of discrete group $G$ and its subgroup $H$. We show that a quasi-Hermitian pair is amenable in the sense of Eymard.