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Positive Herz–Schur multipliers and approximation properties of crossed products
Published online by Cambridge University Press: 14 August 2017
Abstract
For a C*-algebra A and a set X we give a Stinespring-type characterisation of the completely positive Schur A-multipliers on κ(ℓ2(X)) ⊗ A. We then relate them to completely positive Herz–Schur multipliers on C*-algebraic crossed products of the form A ⋊α,rG, with G a 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, for A ⋊α,rG.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 165 , Issue 3 , November 2018 , pp. 511 - 532
- Copyright
- Copyright © Cambridge Philosophical Society 2017
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