Constructions preserving $n$-weak amenability of Banach algebras

TL;DR

This paper investigates conditions under which $n$-weak amenability of Banach algebras is preserved by homomorphisms, particularly focusing on cases where the homomorphism has a right inverse.

Contribution

It demonstrates that $n$-weak amenability is preserved under surjective homomorphisms with right inverses, expanding understanding of structural stability in Banach algebras.

Findings

Preservation of $n$-weak amenability with right inverse homomorphisms

Counterexamples where surjective homomorphisms do not preserve $n$-weak amenability

Application to specific classes of Banach algebras

Abstract

A surjective bounded homomorphism fails to preserve $n$-weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.