Beside the triple product induced by ultrapowers on the bidual of a JB-triple, we assign a triple product to the bidual, , of a JB-triple system , and we show that, under some mild conditions, it makes a JB-triple system. To study ternary -weak amenability of , we need to improve the module structures in the category of JB-triple systems and their iterated duals, which lead us to introduce a new type of ternary module. We then focus on the main question: when does ternary -weak amenability of imply the same property for In this respect, we show that if the bidual of a JB-triple is ternary -weakly amenable, then is ternary -quasiweakly amenable. However, for a general JB-triple system, the results are slightly different for and , and the case requires some additional assumptions.
"Ternary weak amenability of the bidual of a JB-triple." Banach J. Math. Anal. 11 (3) 676 - 697, July 2017. https://doi.org/10.1215/17358787-2017-0013