Representations of invariant multilinear maps on Hilbert C*-modules

The definition of a completely positive invariant multilinear map from a C* -algebra to another is introduced. We construct the representation of a com pletely positive invariant multilinear map on a Hilbert C*-module without t he bridging maps. This is another extension of the Stinespring's representa tion, which is different from a multilinear representation of Christensen a nd Sinclair. We give the covariant representation of completely positive in variant covariant multilinear maps on a Hilbert C*-module. Further, we inve stigate the order structure of such maps and obtain a generalization of the Radon-Nikodym theorem.