Arens regularity of module actions and weak amenability of Banach algebras

TL;DR

This paper explores the connections between the topological centers of module actions and the weak amenability of Banach algebras, providing insights into their structural properties.

Contribution

It establishes new relationships between topological centers of module actions and weak amenability in Banach algebras.

Findings

Identifies links between topological centers and weak amenability

Provides conditions under which Banach algebras are weakly amenable

Enhances understanding of module actions in Banach algebra theory

Abstract

For Banach left and right module actions, we will establish the relationships between topological centers of module actions with some result in the weak amenability of Banach algebras.