محمد رضا امیدی

n this paper we study $\phi$-biprojectivity and character jounson amenability of some Banach algebras like Beurling algebras and semigroup algebras. In fact 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 prove that $\ell^{1}(S)$ is pseudo-amenable if and only if $\ell^{1}(S)$ is character Johnson-amenable, provided that $S$ is a uniformly locally finite band semigroup. We give some conditions whether $\phi$-biprojectivity ($\phi$-biflatness) of $\ell^{1}(S)$ implies the finiteness (amenability) of $S$, respectively