Abstract
Beside the triple product induced by ultrapowers on the bidual of a JB∗-triple, we assign a triple product to the bidual, E∗∗, of a JB-triple system E, and we show that, under some mild conditions, it makes E∗∗ a JB-triple system. To study ternary n-weak amenability of E∗∗, 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 n-weak amenability of E∗∗ imply the same property for E? In this respect, we show that if the bidual of a JB∗-triple E is ternary n-weakly amenable, then E is ternary n-quasiweakly amenable. However, for a general JB-triple system, the results are slightly different for n=1 and n≥2, and the case n=1 requires some additional assumptions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
