A non-weakly amenable Banach algebra whose bidual is weakly amenable

TL;DR

This paper constructs a Banach algebra that is not weakly amenable itself but has a weakly amenable bidual, providing a counterexample to a long-standing open question from 1996.

Contribution

It presents the first known example of a Banach algebra whose bidual is weakly amenable while the algebra itself is not, resolving an open problem.

Findings

Counterexample to inheritance of weak amenability

Shows bidual can be weakly amenable without the algebra being so

Addresses a 27-year-old open question in Banach algebra theory

Abstract

We answer, in the negative, the question: Does a Banach algebra inherit weak amenability from its bidual?, which was open since 1996.