Left $\phi$-biprojectivity of some classes of abstract Segal algebras

Document Type : Research Paper


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



In this paper, we investigate left $\phi$-biprojectivity of Segal algebras and abstract Segal algebras. We show that for some abstract Segal algebras with some mild conditions left $\phi$-biprojectivity is equivalent with left $\phi$-contractibility. Also, we characterize left $\phi$-biprojectivity of a Segal algebra $S(G)$ in the terms of compactness of $G,$ where $G$ is a locally compact group. We introduce a class of abstract Segal algebras among Triangular Banach algebras. We show that  some abstract Segal algebras related to triangular Banach algebras are not biprojective.


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