Biprojectivity and biflatness of Lau product of Banach algebras defined by a Banach algebra morphism

Let Ï• be a homomorphism from a Banach algebra \(\mathcal B\) to a Banach algebra \(\mathcal A\). We deï¬ne a multiplication on the cartesian product space \(\mathcal A\) × \(\mathcal B\) and obtain a new Banach algebra \(\mathcal A\)×ϕ \(\mathcal B\). We show that biprojectivity as well as biflatness of \(\mathcal A\) ×ϕ \(\mathcal B\) are stable with respect to Ï•. DOI: 10.1017/S000497271400048