Operator valued weights without structure theory

A result of Haagerup, generalizing a theorem of Takesaki, states the follow ing: If N subset of M are von Neumann algebras, then there exists a faithful, no rmal and semi-finite (fns) operator valued weight T: M+ --> <(N+)over cap> if and only if there exist fns weights <(phi)over tilde> on M and phi on N satisfying sigma(t)(phi)(x) = sigma(t)(<(phi)over tilde>)(x)For All x is an element of N, t is an element of R. In fact, T can be chosen such that <(p hi)over tilde> = phi oT; T is then uniquely determined by this condition. We present a proof of the above which does not use any structure theory.