%0 Journal Article
%T On biprojectivity and Connes biprojectivity of a dual Banach algebra with respect to a $w^*$ -closed ideal
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Sahami, Amir
%A Shariati, S. Fatemeh
%A Rostami, Mehdi
%A Aj, Mona
%D 2024
%\ 07/01/2024
%V 5
%N 3
%P 225-231
%! On biprojectivity and Connes biprojectivity of a dual Banach algebra with respect to a $w^*$ -closed ideal
%K $I$-Connes biprojctivity
%K Left $\phi$-contractibility
%K Dual Banach algebras
%R 10.22060/ajmc.2023.22285.1149
%X 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.
%U https://ajmc.aut.ac.ir/article_5164_8045577d0a3d1f2213c1003fc44fdfc6.pdf