ABSTRACT
From Lemmas 3 and 7 it follows that the triple (ca, fa, ba) gives rise to a unitary representation ua = Uc",/a,h" of type (S) of G into SVa.
Now, for any x in the manifold X endowed with a nonatomic positive measure J.L, let V~ = Va, f~ = fa, b': = b'"-, and c': = ca; we get the J.Lc.t.p.-guadruple [( v~xEX' (f~)xE\' (b':)xEX' (c':)xEX] which yields the C.t.p.U.f. U~ = Ucn)a,iP on SV~, with
Let a be in cf;•; from Lemma 7, it follows that, for all g in !2/l(X, G), iP(g): x~ ba(g(x)) is an clement of9ll(X, V0 ), and that !Ja:g~ !Ja(g) is a continuous homomorphism from 9ll(X, G) into 9ll(X, Va).
