Weak module amenability of triangular Banach algebras

Rok, strany: 2011, 949 - 958

Let $A$ and $B$ be unital Banach algebras and let $M$ be a unital Banach $A, B$-module. Forrest and Marcoux [F2] have studied the weak amenability of triangular Banach algebra $\mathcal{T}= [ \begin{smallmatrix} A & M & B \end{smallmatrix} ]$ and showed that $\mathcal{T}$ is weakly amenable if and only if the corner algebras $A$ and $B$ are weakly amenable. When $\mathfrak A$ is a Banach algebra and $A$ and $B$ are Banach $\mathfrak A$-module with compatible actions, and $M$ is a commutative left Banach $\mathfrak A$-A-module and right Banach $\mathfrak A$-B-module, we show that $A$ and $B$ are weakly $\mathfrak A$-module amenable if and only if triangular Banach algebra $\mathcal{T}$ is weakly $\mathfrak{T}$-module amenable, where $ \mathfrak{T}:= \{[ \begin{smallmatrix} α & & α \end{smallmatrix} ]: α \in \mathfrak A \}$

ISO 690:

Pourabbas, A., Nasrabadi, E. 2011. Weak module amenability of triangular Banach algebras. In Mathematica Slovaca, vol. 61, no.6, pp. 949-958. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0061-y

APA:

Pourabbas, A., Nasrabadi, E. (2011). Weak module amenability of triangular Banach algebras. Mathematica Slovaca, 61(6), 949-958. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0061-y