  Grothendieck's inequalities for operators and bilinear forms imply some
factorization results for complex m x n matrices. Based on the theory of
operator spaces and completely bounded mappings we present norm optimal
versions of these results and two norm optimal factorization results related to
the Schur product. We show that the spaces of respectively bilinear forms and
Schur multipliers are conjugate duals to each other with respect to their
completely bounded norms.
