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On biprojectivity and Connes biprojectivity of a dual Banach algebra with respect to a $w^*$ -closed ideal | ||
| AUT Journal of Mathematics and Computing | ||
| دوره 5، شماره 3، 2024، صفحه 225-231 اصل مقاله (412.49 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2023.22285.1149 | ||
| نویسندگان | ||
| Amir Sahami* 1؛ S. Fatemeh Shariati2؛ Mehdi Rostami2؛ Mona Aj3 | ||
| 1Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516, Ilam, Iran | ||
| 2Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran | ||
| 3Department of Mathematics, Farhangian University of Kermanshah, Kermanshah, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| $I$-Connes biprojctivity؛ Left $\phi$-contractibility؛ Dual Banach algebras | ||
| مراجع | ||
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