Normal expectations in von Neumann algebras

Let h and k be two Hubert spaces, h®k will denote the tensor product of h and k.Let S/ be a von Neumann algebra acting on h.Let f be an ampliation of Sf in h®k, i.e., ^ is a map of Szf into bounded linear operators of h ® & and f(J^) = Sf®h (/* is the identity map on fc).Let J^ be the image of Sxf by f.The purpose of this paper is to prove the following result: If & is a subalgebra of J^ and if & is the range of a normal expectation ψ defined on S/, then there exists an ampliation of Sf in h ® fc, independent of ^ and of 9, such that φ®h is a spatial isomorphism of