(2n − 1)-Ideal amenability of triangular banach algebras

Abstract

Let \(\mathcal {A}\) and \(\mathcal {B}\) be two unital Banach algebras and let \(\mathcal {M}\) be an unital Banach \(\mathcal {A}, \mathcal {B}\)-module. Also, let \(\mathcal {T}=\left [\begin {array}{cc} \mathcal {A} & \mathcal {M} \\ & \mathcal {B} \end {array}\right ]\) 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 \(\mathcal {T}\) for all n≥1. We introduce the structure of ideals of these Banach algebras and then, we show that (2n−1)-ideal amenability of \(\mathcal {T}\) depends on (2n−1)-ideal amenability of Banach algebras \(\mathcal {A}\) and \(\mathcal {B}\).