## Banach Journal of Mathematical Analysis

### Some homological and cohomological notions on $T$-Lau product of Banach algebras

#### Abstract

Let $\mathcal A$ and $\mathcal B$ be Banach algebras and let $T:{\mathcal B}\rightarrow{\mathcal A}$ be a continuous homomorphism. Recently, we introduced a product ${\mathcal M}:={\mathcal A}\times_T{\mathcal B}$, which is a strongly splitting Banach algebra extension of $\mathcal B$ by $\mathcal A$. In the present paper, we characterize biprojectivity, approximate biprojectivity and biflatness of ${\mathcal A}\times_T{\mathcal B}$ in terms of ${\mathcal A}$ and ${\mathcal B}$. We also study some notions of amenability such as approximate amenability and pseudo-amenability of ${\mathcal A}\times_T{\mathcal B}$.

#### Article information

Source
Banach J. Math. Anal., Volume 9, Number 2 (2015), 183-195.

Dates
First available in Project Euclid: 19 December 2014

https://projecteuclid.org/euclid.bjma/1419001112

Digital Object Identifier
doi:10.15352/bjma/09-2-13

Mathematical Reviews number (MathSciNet)
MR3296113

Zentralblatt MATH identifier
1312.43001

#### Citation

Nemati, Mehdi; Javanshiri, Hossein. Some homological and cohomological notions on $T$-Lau product of Banach algebras. Banach J. Math. Anal. 9 (2015), no. 2, 183--195. doi:10.15352/bjma/09-2-13. https://projecteuclid.org/euclid.bjma/1419001112

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