Authors | Ebrahim Nasrabadi |
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Journal | Journal of the Indian Mathematical Society |
Page number | 272-285 |
Serial number | 86 |
Volume number | 3 |
Paper Type | Full Paper |
Published At | 2019 |
Journal Grade | ISI |
Journal Type | Typographic |
Journal Country | India |
Journal Index | Scopus |
Abstract
Let $A$ and $B$ be unital Banach algebras and $M$ be an unital Banach $A, B$-module. In this paper we define the concept of the $(n)$-ideal module amenability of Banach algebras and investigate the relation between the $(2n-1)$-ideal module amenability of triangular Banach algebra $\mathcal T=\left[\begin{array}{rr} A & M \\ & B \end{array} \right]$ (as a $ \mathfrak{T}=\set{\Mat{\alpha}{}{\alpha}; \alpha\in \mathfrak{A}} $-module) and $(2n-1)$-ideal module amenability of $A$ and $B$ (as an $\mathfrak{A}$-module). Finally, in the case that $A=B=M=\ell^1(S)$, for unital and commutative inverse semigroup $S$ with idempotent set $E$, we show that %$\left[\begin{array}{rr} \ell^1(S) & \ell^1(S) \\ & \ell^1(S)\end{array} \right]$ $\mathcal T$ as a $\mathfrak{T}$-module is $(2n-1)$-ideal module amenable while is not module amenable.
tags: Ideal module amenability, Inverse semigroup algebras, Module amenability, Triangular Banach algebras.