The Central Haagerup Tensor Product and Maps between von Neumann Algebras

We introduce the central Haagerup tensor product R ⊗ Fh R for a von Neumann algebra R, and we show that the natural injection into tbe space CB(R, R) of completely bounded maps on R is isometric. This is used to study mappings between von Neumann algebras and to give a new characterization of injectivity. This tensor product is also studied for C*-algebras A, and we show that the injection into CB(A, A) need not always be isometric, depending on the topology of the primitive ideal space of A.