Ternary n-weak amenability of certain commutative Banach algebras and 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 C*-algebra. We also show that every commutative 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.