Positive definite maps on amenable groups, II

TL;DR

This paper introduces an Ulam-type stability condition for positive definite maps on countable groups and demonstrates that this condition characterizes the property of amenability in these groups.

Contribution

It establishes a novel stability condition that precisely characterizes amenability for positive definite maps on countable groups.

Findings

The stability condition characterizes amenability.

Positive definite maps satisfying the condition relate to group properties.

Provides a new criterion for amenability in countable groups.

Abstract

We introduce an Ulam-type stability condition for positive definite maps defined on a countable group and prove that this condition characterizes amenability.