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BIPROJECTIVITY AND BIFLATNESS OF LAU PRODUCT OF BANACH ALGEBRAS DEFINED BY A BANACH ALGEBRA MORPHISM
Abstract Let ${\it\varphi}$ be a homomorphism from a Banach algebra ${\mathcal{B}}$ to a Banach algebra ${\mathcal{A}}$ . We define a multiplication on the Cartesian product space ${\mathcal{A}}\times {\mathcal{B}}$ and obtain a new Banach algebra ${\mathcal{A}}\times _{{\it\varphi}}{\mathcal{B}}$ . We show that biprojectivity as well as biflatness of ${\mathcal{A}}\times _{{\it\varphi}}{\mathcal{B}}$ are stable …