Approximate biprojectivity of Banach algebras with respect to their character spaces

Document Type : Research Paper


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

2 Department of Basic Sciences, Kermanshah University of Technology, Kermanshah, Iran



    In this paper we introduce approximate $\phi$-biprojective Banach algebras, where $\phi$ is a non-zero character. We show that for SIN group $G$, the group algebra $L^{1}(G)$ is approximately $\phi$-biprojective if and only if $G$ is amenable, where $\phi$ is the augmentation character. Also we show that the Fourier algebra $A(G)$ over a locally compact $G$ is always approximately $\phi$-biprojective.


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