Seemingly Injective Von Neumann Algebras

We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only it is seemingly injective in following sense: there factorization of identity M $$I{d_M} = vu:M\buildrel u \over \longrightarrow B(H)\buildrel v M$$ with normal, unital, completely contractive. As corollary, separable predual, isomorphic (as Banach space) to B(ℓ2). For instance this applies (rather surprisingly) any free group. Nevertheless, since B(H) fails (due Szankowski) are M’s (namely B(H)** certain finite examples defined using ultraproducts) not injective. Moreover, for be suffices have above IdM through u, (and still normal).