Ternary weak amenability of the bidual of a JB*-triple

AuthorsMohsen Niazi,
JournalBanach Journal of Mathematical Analysis
Page number676-697
Serial number11
Volume number3
IF0.967
Paper TypeFull Paper
Published At2017
Journal GradeISI
Journal TypeElectronic
Journal CountryIran, Islamic Republic Of
Journal IndexJCR،Scopus

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.

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tags: Jordan Banach triple, JB*-triple, Banach ternary module, triple derivation, ternary weak amenability