On certain products of Banach algebras with applications to harmonic analysis

Abstract

Given Banach algebras $A$ and $B$ with spectrum $\sigma (B)\ne \emptyset$, and given $\theta \in \sigma (B)$, we define a product $A\mathbin{\times_{\theta}} B$, which is a strongly splitting Banach algebra extension of $B$ by $A$. We obtain characte