An approximate notion in the homology of the enveloping dual Banach algebras
نویسندگان
1 Department of Mathematics, Faculty of Basic Science, Ilam University, P.O. Box 69315-516, Ilam, Iran
2 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
3 Department of Mathematics, West Tehran Branch, Islamic Azad University, Tehran, Iran
doi
10.22034/as.2024.21666.1718چکیده
In this paper, we introduce a notion of approximate $WAP$-biprojectivity for the enveloping dual Banach algebras. We also find some relations between approximate Connes amenability, approximate biprojectivity, left $\varphi$-contractibility and approximate $WAP$-biprojectivity. Moreover, we propose a criterion to show that the enveloping dual Banach algebras associated to triangular Banach algebras are not approximately $WAP$-biprojective. Finally, we present some examples of the enveloping dual Banach algebras associated to $l^1(S)$ and $\ell^1(\mathbb{N})$ (equipped with a new multiplication) and also study their approximate $WAP$-biprojectivity, where $S$ is a unital weakly cancellative semigroup.
