Representations of completely bounded multilinear operators

A definition of a completely bounded multilinear operator from one C^*-algebra into another is introduced. Each completely bounded multilinear operator from a C^*-algebra into the algebra of bounded linear operators on a Hilbert space is shown to be representable in terms of ^*-representations of the C^*-algebra and interlacing operators. This result extends Wittstock's Theorem that decomposes a completely bounded linear operator from a C^*-algebra into an injective C^*-algebra into completely positive linear operators.