Relations between ideals of the figa-Talamanca herz algebra A<inf>p</inf>(G) of a locally compact group G and ideals of A<inf>p</inf>(H) of a closed subgroup

Let G be a locally compact group and H a closed subgroup. In analogy with the classical case,we obtain the two following results. Suppose at first that G is amenable and that I is a closed ideal of Ap (H) having a bounded approximate unit, then the ideal {u € Ap(G)|Reshu €I} of Ap(G) also has a bounded approximate unit. The second result concerns the closedness of { Reshu €I I} in Ap(H) for a closed ideal I of Ap(G). We show that this set is closed if H is amenable.