The Bochner-Eberlein-Doss property for θ-Lau product of Banach algebras

Let (A,∥⋅∥A) and (B,∥⋅∥B) be two commutative Banach algebras with nonempty character spaces and θ∈Δ(B). The aim of this paper is to verify the BED property for the θ-Lau product of A and B, denoted by A×θB, whenever A and B are non-unital and semisimple. First, along with all available results regarding θ-Lau product of Banach algebras, we prove that A×θB is without order if and only if B is so. Then as the main result of the present work, we establish that A×θB is a BED algebra if and only if Ae and B are so.