Positive definite maps on amenable groups

TL;DR

This paper characterizes amenability of groups using positive definite functions valued in a von Neumann algebra, providing new insights into the structure of amenable groups.

Contribution

It introduces conditions linking amenability to positive definite functions with values in von Neumann algebras, a novel approach in the field.

Findings

Characterization of amenability via positive definite functions

Conditions involving von Neumann algebra-valued functions

New criteria for identifying amenable groups

Abstract

We describe conditions that characterize amenability for groups in terms of positive definite functions valued in a von Neumann algebra.