Let A, B, and C be Banach algebras, α ∈ Hom(A, B) and β ∈ Hom(C, B), and kαk ≤ 1, kβk ≤ 1. We define the Banach algebra A ×α B ×β C by new product on A × B × C which is a strongly splitting extension of C by B. We show that these products from a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Then we consider spectrum, Arens regularity, amenability and weak amenability of these products.
