  Let (M,N) be a pair of von Neumann algebras, or of dual operator spaces with
at least one of them having property S_\sigma, and let T be an arbitrary
completely bounded mapping on M. We present an explicit construction of an
amplification of T to a completely bounded mapping on the w^*-spatial tensor
product of M and N. Our approach makes essential use of the description of the
predual of the latter given by Effros and Ruan in terms of the projective
operator space tensor product and is further based on the concept of slice maps
as introduced by Tomiyama. We discuss several properties of an amplification in
connection with the investigations made by May-Neuhardt-Wittstock, where the
special case M=B(H) and N=B(K) has been considered (for Hilbert spaces H and
K). We will then mainly focus on various applications, such as a purely
algebraic characterization of w^*-continuity using amplifications, as well as a
generalization of the so-called Ge-Kadison Lemma (in connection with the
uniqueness problem of amplifications). Our study will eventually enable us to
show that the essential assertion of the main result obtained in the
above-mentioned work of May-Neuhardt-Wittstock concerning completely bounded
bimodule homomorphisms actually relies on a basic property of Tomiyama's slice
maps.
