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In: Mathematica Slovaca, vol. 69, no. 2
Ebrahim Nasrabadi

Weak module amenability of triangular Banach algebras II

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Year, pages: 2019, 425 - 432
Keywords: weak amenability, module derivation, module amenability, weak module amenability, triangular Banach algebras

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Let $A$ and $B$ be Banach $\mathfrak{A}$-bimodule and Banach $\mathfrak{B}$-bimodule algebras, respectively. Also let $M$ be a Banach $A, B$-module and Banach $\mathfrak{A},\mathfrak{B}$-module with compatible actions. In the case of $\mathfrak{A}= \mathfrak{B}$, the author along with Pourabbas [PN] have studied the weak $\mathfrak{A}$-module amenability of triangular Banach algebra $\mathcal{T}=[\begin{array}{rr} A & M & B\end{array}]$ and showed that $\mathcal{T}$ is weakly $\mathfrak{A}$-module amenable if and only if the corner Banach algebras $A$ and $B$ are weakly $\mathfrak{A}$-module amenable, where $A$, $B$ and $M$ are unital. In this paper we investigate a special structure of $\mathfrak{A}\oplus\mathfrak{B}$-bimodule derivation from $\mathcal{T}$ into $\mathcal{T}*$ and show that $\mathcal{T}$ is weakly $\mathfrak{A}\oplus\mathfrak{B}$-bimodule amenable if and only if the corner Banach algebras $A$ and $B$ are weakly $\mathfrak{A}$-module amenable and weakly $\mathfrak{B}$-module amenable, respectively, where $A$, $B$ and $M$ are essential and not necessary unital.

How to cite:

ISO 690:
Nasrabadi, E. 2019. Weak module amenability of triangular Banach algebras II. In Mathematica Slovaca, vol. 69, no.2, pp. 425-432. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0234

APA:
Nasrabadi, E. (2019). Weak module amenability of triangular Banach algebras II. Mathematica Slovaca, 69(2), 425-432. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0234

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Published: 27. 3. 2019