Open Access
2015 Some homological and cohomological notions on $T$-Lau product of Banach algebras
Hossein Javanshiri, Mehdi Nemati
Banach J. Math. Anal. 9(2): 183-195 (2015). DOI: 10.15352/bjma/09-2-13


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 ${\mathcal A}\times_T{\mathcal B}$.


Download Citation

Hossein Javanshiri. Mehdi Nemati. "Some homological and cohomological notions on $T$-Lau product of Banach algebras." Banach J. Math. Anal. 9 (2) 183 - 195, 2015.


Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1312.43001
MathSciNet: MR3296113
Digital Object Identifier: 10.15352/bjma/09-2-13

Primary: ‎43A07‎
Secondary: 46H25

Keywords: approximate amenability , approximate biprojectivity , biflatness , Biprojectivity , pseudo-amenability

Rights: Copyright © 2015 Tusi Mathematical Research Group

Vol.9 • No. 2 • 2015
Back to Top