Amenability and invariant subspaces of the algebra of $\Psi$-pseudomeasures

Let G be a locally compact group, and let (\Phi,\Psi) be a complementary pair of Young functions satisfying the \Delta_{2} -condition. In this article, we consider PM_{\Psi}(G) the Banach algebra of \Psi -pseudomeasures along with its predual, the Orlicz Figà-Talamanca Herz algebra A_{\Phi}(G) . We prove sufficient conditions for the amenability of G in terms of the norm closed topologically invariant subspaces of PM_{\Psi}(G) . Further, when G is amenable and the Young function \Phi satisfies the MA condition, we establish a one-to-one correspondence between certain topologically invariant subalgebras of PM_{\Psi}(G) and the closed subgroups of G . A similar result is obtained for A_{\Phi}(G) , where we derive a bijection between certain topologically invariant subalgebras of A_{\Phi}(G) and the compact subgroups of G .