Positive Herz-Schur multipliers and approximation properties of crossed products
Journal article, 2017

For a C*-algebra A and a set X we give a Stinespring-type characterisation of the completely positive Schur A -multipliers on K(ℓ^2(X))⊗A . We then relate them to completely positive Herz-Schur multipliers on C ∗ -algebraic crossed products of the form A⋊ α,r G , with G a discrete group, whose various versions were considered earlier by Anantharaman-Delaroche, Bedos 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,r G .

Author

Andrew McKee

Queen's University Belfast

Adam Skalski

Polish Academy of Sciences

I. G. Todorov

Queen's University Belfast

Lyudmyla Turowska

University of Gothenburg

Chalmers, Mathematical Sciences

Mathematical Proceedings of the Cambridge Philosophical Society

0305-0041 (ISSN) 1469-8064 (eISSN)

Vol. 165 3 511-532

Subject Categories

Mathematics

Roots

Basic sciences

DOI

10.1017/S0305004117000639

More information

Latest update

11/30/2018