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A note on left $φ$-biflat Banach algebrasMay 14 2019In this paper, we study the notion of $\phi$-biflatness for some Banach algebras, where $\phi$ is a non-zero multiplicative linear functional. We show that the Segal algebra $S(G)$ is left $\phi$-biflat if and only if $G$ is amenable. Also, we characterize ... More

On left $φ$-biprojectivity and left $φ$-biflatness of certain Banach algebrasMay 14 2019In this paper, we study left $\phi$-biflatness and left $\phi$-biprojectivity of some Banach algebras, where $\phi$ is a non-zero multiplicative linear function. We show that if the Banach algebra $A^{**}$ is left $\phi$-biprojective, then $A$ is left ... More

On homological notions of Banach algebras related to a characterJan 11 2014Sep 08 2018In this paper, we countinue our work in \cite{11}. We show that $L^{1}(G,w)$ is $\phi_{0}$-biprojective if and only if $G$ is compact, where $\phi_{0}$ is the augmentation character. We introduce the notions of character Johnson amenability and character ... More

Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimoduleMay 29 2003Nov 17 2003Let $A$ be a dual Banach algebra with predual $A_\ast$ and consider the following assertions: (A) $A$ is Connes-amenable; (B) $A$ has a normal, virtual diagonal; (C) $A_\ast$ is an injective $A$-bimodule. For general $A$, all that is known is that (B) ... More