Ternary n-Weak Amenability of Certain Commutative Banach Algebras and \(\hbox {JBW}^*\)-Triples

Abstract

We show that a commutative unital Banach *-algebra is ternary n-weakly amenable when it is n-weakly amenable. We apply this result for a wide variety of commutative n-weakly amenable algebras such as for a convolution group algebra on a discrete abelian group and for a commutative unital \(\hbox {C}^*\)-algebra. We also show that every commutative \(\hbox {JBW}^*\)-triple is ternary n-weakly amenable. These results present a somehow unified extension of the previous ternary weak amenability results in the category of triple systems and n-weak amenability results in the category of Banach algebras.

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Acknowledgements

We would like to thank the anonymous referees for their constructive comments and suggestions.

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Correspondence to Ali Akbar Khadem-Maboudi.

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Communicated by Hamid Reza Ebrahimi Vishki.

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Niazi, M., Khadem-Maboudi, A.A. & Miri, M.R. Ternary n-Weak Amenability of Certain Commutative Banach Algebras and \(\hbox {JBW}^*\)-Triples. Bull. Iran. Math. Soc. 46, 1791–1800 (2020). https://doi.org/10.1007/s41980-020-00359-9

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Keywords

  • \(\hbox {JB}^*\)-triple
  • Ternary module
  • Ternary derivation
  • n-Weak amenability of Banach algebras
  • Ternary n-weak amenability

Mathematics Subject Classification

  • 17C65
  • 46K70
  • 46H25