Banach Journal of Mathematical Analysis, ( ISI ), Year (2017-10)

Title : ( Ternary Weak Amenability of the Bidual of a JB*-Triple )

Authors: Mohsen Niazi , Mohammad Reza Miri , Hamid Reza Ebrahimi Vishki ,

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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 $n$-quasi-weakly amenable‎. ‎For a general JB-triple system‎, ‎however‎, ‎the results are slightly different for $n=1$ and $n\geq2$‎, ‎and the case $n=1$ requires some additional assumptions‎.

Keywords

, Jordan Banach triple‎, ‎JB$^*$-triple‎, ‎Banach ternary module‎, ‎triple derivation‎, ‎ternary weak amenability
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@article{paperid:1059016,
author = {Mohsen Niazi and Mohammad Reza Miri and Ebrahimi Vishki, Hamid Reza},
title = {Ternary Weak Amenability of the Bidual of a JB*-Triple},
journal = {Banach Journal of Mathematical Analysis},
year = {2017},
month = {October},
issn = {1735-8787},
keywords = {Jordan Banach triple‎; ‎JB$^*$-triple‎; ‎Banach ternary module‎; ‎triple derivation‎; ‎ternary weak amenability},
}

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%0 Journal Article
%T Ternary Weak Amenability of the Bidual of a JB*-Triple
%A Mohsen Niazi
%A Mohammad Reza Miri
%A Ebrahimi Vishki, Hamid Reza
%J Banach Journal of Mathematical Analysis
%@ 1735-8787
%D 2017

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