Abstract
For aC*-algebraAand a setXwe give a Stinespring-type characterisation of the completely positive SchurA-multipliers on κ(ℓ2(X)) ⊗A. We then relate them to completely positive Herz–Schur multipliers onC*-algebraic crossed products of the formA⋊α,rG, withGa discrete group, whose various versions were considered earlier by Anantharaman-Delaroche, Bédos and Conti, and Dong and Ruan. The latter maps are shown to implement approximation properties, such as nuclearity or the Haagerup property, forA⋊α,rG.
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