On biprojectivity and Connes biprojectivity of a dual Banach algebra with respect to a $w^*$ -closed ideal

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516, Ilam, Iran

2 Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran

3 Department of Mathematics, Farhangian University of Kermanshah, Kermanshah, Iran

Abstract

In this paper, we introduce a notion of Connes biprojectivity for a dual Banach algebra $A$ with respect to its $w^{*}$-closed ideal $I$, say $I$-Connes biprojectivity. Some Lipschitz algebras $Lip_{\alpha}(X)$ and some matrix algebras are studied under this new notion. Also, with some mild assumptions, the relation between $I$-Connes biprojectivity and left $\phi$-contractibility is given, where $\phi$ is a $w^{*}$-continuous multiplicative linear functional on $A$. As an application, we characterize Connes biprojectivity of some Lipschitz algebras.

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References

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AUT Journal of Mathematics and Computing
Volume 5, Issue 3
July 2024
Pages 225-231

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