A Stinespring type theorem for completely positive multilinear maps on Hilbert C*-modules

Abstract

We extend the Stinespring's representation theorem for two k-linear maps on a Hilbert C*-module and a C*-algebra. We prove a covariant representation theorem for two covariant k-linear maps and construct the extension of two k-linear maps to the crossed product Hilbert C*-module and the crossed product C*-algebra.