Maximal regular ideals of algebras related to the dual of Orlicz Fig\`{a}-Talamanca Herz algebra

Let G be a locally compact group and the pair (Φ,Ψ) be a complementary pair of Young functions satisfying the Δ₂-condition. Let A_Φ(G) be the Orlicz analog of the Fig\`{a}-Talamanca Herz algebra associated with the function Φ. The dual of the algebra A_Φ(G) is the space of Ψ-pseudomeasures, denoted PM_Ψ(G). In this article, we aim to characterize the maximal regular left (right or two-sided) ideals of the Banach algebras A' and B''. The space A is any of the closed subspaces Cδ,Ψ(G), PF_Ψ(G), M(G), AP_Ψ(G), WAP_Ψ(G), UCB_Ψ(G) or PM_Ψ(G), of PM_Ψ(G), and the space B is any of the Banach algebras W_Φ(G) or B_Φ(G). We further characterize the minimal left ideals of A'. Moreover, we also prove the necessary and sufficient conditions for the existence of minimal ideals in the Banach algebras A_Φ(G) and B.