P-PSEUDOMEASURES AND CLOSED SUBGROUPS

Let PM(p)(G) be the space of all p-pseudomeasures on a locally compact group G. We show the existence of a conditional expectation from PM(p )(G) onto PM(p)(H) where H is a closed normal subgroup of G. As an app lication we give a new proof of the fact that H is a set of p-synthesi s in G; we also get an inequality involving the operator norm of bound ed measures on G. Moreover, in analogy with a theorem of Reiter, we ob tain a result concerning the closed ideals of the Figa-Talamanca Herz algebra of G.