Open Access
July 2017 Ternary weak amenability of the bidual of a JB-triple
Mohsen Niazi, Mohammad Reza Miri, Hamid Reza Ebrahimi Vishki
Banach J. Math. Anal. 11(3): 676-697 (July 2017). DOI: 10.1215/17358787-2017-0013


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 n2, and the case n=1 requires some additional assumptions.


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Mohsen Niazi. Mohammad Reza Miri. Hamid Reza Ebrahimi Vishki. "Ternary weak amenability of the bidual of a JB-triple." Banach J. Math. Anal. 11 (3) 676 - 697, July 2017.


Received: 1 August 2016; Accepted: 18 October 2016; Published: July 2017
First available in Project Euclid: 9 June 2017

zbMATH: 06754308
MathSciNet: MR3679901
Digital Object Identifier: 10.1215/17358787-2017-0013

Primary: 17C65
Secondary: 17A40 , 46H25 , 46H70 , 46K70 , 46L05 , 47B47

Keywords: Banach ternary module , JB$^{*}$-triple , Jordan Banach triple , ternary weak amenability , triple derivation

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 3 • July 2017
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