Module amenability, module character biprojectivity and module character biflatness of generalize Lau product of two Banach algebras

Abstract

‎Let $\mathfrak{A}$ be a Banach algebra and $T$ be an $\mathfrak{A}$-module homomorphism from $\mathfrak{A}$-bimodule $B$ into $\mathfrak{A}$-bimodule $A$‎. ‎We investigate module amenability (resp‎. ‎module approximate amenability)‎, ‎module character amenability (resp‎. ‎module character approximate amenability)‎, ‎module character biprojectivity and module character biflatness of $A\times_{T_{\mathfrak{A}}} B$ for every two Banach $\mathfrak{A}$-bimodule $ A$ and $B$‎.