فهرست نشریات علمی دسترسی آزاد ایران

In the current investigation, we find some necessary and sufficient conditions for the triangular Banach algebra $T=\begin{bmatrix}A&\mathbb M\\0&B\end{bmatrix}$ to be module amenable, module biprojective and module biflat (as $\mathcal U\oplus \mathcal U$-module), where $A$ and $B$ are Banach $\mathcal U$-bimodules and $\mathbb M$ is a Banach $A,B$-module and Banach $\mathcal U$-module with compatible actions. As an application, we show that for an inverse semigroup $S$ with the set of idempotents $E$, under what conditions $\begin{bmatrix}l^1(S)&\\& l^1(S)\end{bmatrix}$ is module amenable, module biprojective and module biflat (as $l^1(E)\oplus l^1(E)$-module).