$\Delta$-weak character amenability of certain Banach algebras

TL;DR

This paper introduces the concept of Δ-weak character amenability in Banach algebras and explores its properties in various algebraic constructions such as tensor products, Lau products, Segal algebras, and module extensions.

Contribution

It defines Δ-weak character amenability and investigates its presence in several classes of Banach algebras, expanding the understanding of amenability properties.

Findings

Δ-weak character amenability is established for tensor products of Banach algebras.

The paper shows conditions under which Lau products are Δ-weak character amenable.

Results include the Δ-weak character amenability of certain Segal and module extension Banach algebras.

Abstract

In this paper we introduce the notion of $\Delta$-weak character amenable Banach algebras and investigate $\Delta$-weak character amenability of certain Banach algebras such as projective tensor product $A\widehat{\otimes}B$, Lau product $A\times_TB$ for every Banach algebra $ A$ and $B$, where $T$ be a homomorphism from $B$ into $A$, abstract Segal algebras and module extension Banach algebras.