$n$-weak module amenability of triangular Banach algebras

Rok, strany: 2015, 645 - 666

Let $\mathcal A$, $\mathcal B$ be Banach $\mathfrak A$-modules with compatible actions and $\mathcal M$ be a left Banach $\mathcal A$-$\mathfrak A$-module and a right Banach $\mathcal B$-$\mathfrak A$-module. In the current paper, we study module amenability, $n$-weak module amenability and module Arens regularity of the triangular Banach algebra $\mathcal T= [\begin{matrix} \mathcal A & \mathcal M \\ & \mathcal B \end{matrix}]$ (as an $\mathfrak T:= \{[\begin{matrix} \alpha & \\ & \alpha \end{matrix}] \mid \alpha\in\mathfrak A\}$-module). We employ these results to prove that for an inverse semigroup $S$ with subsemigroup $E$ of idempotents, the triangular Banach algebra $\mathcal T_0=[\begin{matrix}\ell^1(S)& \ell^1(S) \\ & \ell^1(S) \end{matrix}]$ is permanently weakly module amenable (as an $\mathfrak T_0= [\begin{matrix} \ell^1(E)& \\ & \ell^1(E) \end{matrix}]$-module). As an example, we show that $\mathcal T_0$ is $\mathfrak T_0$-module Arens regular if and only if the maximal group homomorphic image $G_S$ of $S$ is finite.

ISO 690:

Bodaghi, A., Jabbari, A. 2015. $n$-weak module amenability of triangular Banach algebras. In Mathematica Slovaca, vol. 65, no.3, pp. 645-666. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0045

APA:

Bodaghi, A., Jabbari, A. (2015). $n$-weak module amenability of triangular Banach algebras. Mathematica Slovaca, 65(3), 645-666. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0045