Weak amenability for dynamical systems

TL;DR

This paper introduces the concept of weak amenability for C*- and W*-dynamical systems using Herz--Schur multipliers, extending known group results to operator algebraic systems.

Contribution

It develops a new framework for weak amenability in dynamical systems via Herz--Schur multipliers, generalizing classical group results to C*- and W*-algebras.

Findings

Recovered Haagerup's characterization of weak amenability for discrete groups.

Extended the Fourier algebra concept to crossed products.

Studied multipliers of the generalized Fourier algebra.

Abstract

Using the recently developed notion of a Herz--Schur multiplier of a C*-dynamical system we introduce weak amenability of C*- and W*-dynamical systems. As a special case we recover Haagerup's characterisation of weak amenability of a discrete group. We also consider a generalisation of the Fourier algebra to crossed products and study its multipliers.