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arXiv · 1905.05552

On left $ϕ$-biprojectivity and left $ϕ$-biflatness of certain Banach algebras

Amir Sahami
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Abstract

In this paper, we study left $ϕ$-biflatness and left $ϕ$-biprojectivity of some Banach algebras, where $ϕ$ is a non-zero multiplicative linear function. We show that if the Banach algebra $A^{**}$ is left $ϕ$-biprojective, then $A$ is left $ϕ$-biflat. Using this tool we study left $ϕ$-biflatness of some matrix algebras. We also study left $ϕ$-biflatness and left $ϕ$-biprojectivity of the projective tensor product of some Banach algebras. We prove that for a locally compact group $G$, $M(G)\otimes_{p} A(G)$ is left $ϕ\otimes ψ$-biprojective if and only if $G$ is finite. We show that $M(G)\otimes_{p} L^1(G)$ is left $ϕ\otimes ψ$-biprojective if and only if $G$ is compact.

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Amir Sahami. 2019-05-14. On left $ϕ$-biprojectivity and left $ϕ$-biflatness of certain Banach algebras. https://arxiv.org/abs/1905.05552

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