Jordan Ideals of Vector-Valued Beurling Algebras and θ-Lau Product of Banach Algebras

In this paper, we give a characterization of the closed Jordan ideals of vector-valued Beurling algebras L1(G,A,ω) and the direct sum of Banach algebras. We also investigate Jordan ideals of the θ-Lau product of Banach algebras and give some results about Banach algebras A♯ and A⊕B. We also prove that every Jordan ideal of A⊕B is an ideal if and only if every Jordan ideal of A and B is an ideal of A and B, respectively, where A is a unital Banach algebra and B is any Banach algebra. Finally, we apply our results to some Banach algebras related to a locally compact group.