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\begin{document}$\mathcal {A}$\end{document} and ℬ\documentclass[12pt]{minimal}
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\begin{document}$\mathcal {B}$\end{document} be two unital Banach algebras and let ℳ\documentclass[12pt]{minimal}
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\begin{document}$\mathcal {M}$\end{document} be an unital Banach A,ℬ\documentclass[12pt]{minimal}
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\begin{document}$\mathcal {A}, \mathcal {B}$\end{document}-module. Also, let T=Aℳℬ\documentclass[12pt]{minimal}
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\begin{document}$\mathcal {T}=\left [\begin {array}{cc} \mathcal {A} & \mathcal {M} \\ & \mathcal {B} \end {array}\right ]$\end{document} be the corresponding triangular Banach algebra. Forrest and Marcoux (Trans. Amer. Math. Soc.354 (2002) 1435–1452) have studied the n-weak amenability of triangular Banach algebras. In this paper, we investigate (2n−1)-ideal amenability of T\documentclass[12pt]{minimal}
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\begin{document}$\mathcal {T}$\end{document} for all n≥1. We introduce the structure of ideals of these Banach algebras and then, we show that (2n−1)-ideal amenability of T\documentclass[12pt]{minimal}
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\begin{document}$\mathcal {T}$\end{document} depends on (2n−1)-ideal amenability of Banach algebras A\documentclass[12pt]{minimal}
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\begin{document}$\mathcal {A}$\end{document} and ℬ\documentclass[12pt]{minimal}
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\begin{document}$\mathcal {B}$\end{document}.