Ternary n-Weak Amenability of Certain Commutative Banach Algebras and $$\hbox {JBW}^*$$-Triples

Abstract

We show that a commutative unital Banach *-algebra is ternary n-weakly amenable when it is n-weakly amenable. We apply this result for a wide variety of commutative n-weakly amenable algebras such as for a convolution group algebra on a discrete abelian group and for a commutative unital $$\hbox {C}^*$$ -algebra. We also show that every commutative $$\hbox {JBW}^*$$ -triple is ternary n-weakly amenable. These results present a somehow unified extension of the previous ternary weak amenability results in the category of triple systems and n-weak amenability results in the category of Banach algebras.