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# Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2018: 0.29

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1337-2211
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Volume 69, Issue 2

# Weak module amenability of triangular banach algebras II

Published Online: 2019-03-19 | DOI: https://doi.org/10.1515/ms-2017-0234

## Abstract

Let A and B be Banach 𝔄-bimodule and Banach 𝔅-bimodule algebras, respectively. Also let M be a Banach A, B-module and Banach 𝔄, 𝔅-module with compatible actions. In the case of 𝔄 = 𝔅, the author along with Pourabbas [5] have studied the weak 𝔄-module amenability of triangular Banach algebra $\begin{array}{}\mathcal{T}=\left[\begin{array}{rr}A& M\\ & B\end{array}\right]\end{array}$ and showed that 𝓣 is weakly 𝔄-module amenable if and only if the corner Banach algebras A and B are weakly 𝔄-module amenable, where A, B and M are unital.

In this paper we investigate a special structure of 𝔄 ⊕ 𝔅-bimodule derivation from 𝓣 into 𝓣 and show that 𝓣 is weakly 𝔄 ⊕ 𝔅-bimodule amenable if and only if the corner Banach algebras A and B are weakly 𝔄-module amenable and weakly 𝔅-module amenable, respectively, where A, B and M are essential and not necessary unital.

MSC 2010: Primary 46H20; Secondary 46H25; 16E40

## References

• [1]

Amini, M.: Module amenability for semigroup algebras, Semigroup Forum 69 (2004), 243–254.Google Scholar

• [2]

Amini, M.—Bagha, B. E.: Weak module amenability for semigroup algebras, Semigroup Forum 71 (2005), 18–26.

• [3]

Forrest, B. E.— Marcoux, L. W.: Weak amenability of triangular Banach algebras, Trans. Amer. Math. Soc. 345 (2002), 1435–1452.Google Scholar

• [4]

Johnson, B. E.: Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).Google Scholar

• [5]

Pourabbas, A. R.— Nasrabadi, E.: Weak module amenability of triangular Banach algebras, Math. Slovaca 61 (2011), 949–958.Google Scholar

Accepted: 2018-07-30

Published Online: 2019-03-19

Published in Print: 2019-04-24

(Communicated by Gregor Dolinar)

Citation Information: Mathematica Slovaca, Volume 69, Issue 2, Pages 425–432, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918,

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