Abstract
Abstract We show that $\ell ^1(\mathbb {N}_\wedge )$ is $\varphi $ -amenable for each multiplicative linear functional $\varphi :\ell ^1(\mathbb {N}_\wedge )\rightarrow \mathbb {C}.$ This is a counterexample to the final corollary of Jaberi and Mahmoodi [‘On $\varphi $ -amenability of dual Banach algebras’, Bull. Aust. Math. Soc.105 (2022), 303–313] and shows that the final theorem in that paper is not valid.
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