On certain products of Banach algebras with applications to harmonic analysis
Given Banach algebras A and B with spectrum σ(B) ≠ ∅, and given θ ∈ σ(B), we define a product , which is a strongly splitting Banach algebra extension of B by A. We obtain characterizations of bounded approximate identities, spectrum, topological center, minimal idempotents, and study the ideal structure of these products. By assuming B to be a Banach algebra in ₀(X) whose spectrum can be identified with X, we apply our results to harmonic analysis, and study the question of spectral synthesis,...