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Positive Herz–Schur multipliers and approximation properties of crossed products

Published online by Cambridge University Press:  14 August 2017

ANDREW MCKEE ,
ADAM SKALSKI ,
IVAN G. TODOROV  and
LYUDMILA TUROWSKA
ANDREW MCKEE
Affiliation:
Mathematical Sciences Research Centre, Queen's University Belfast, Belfast BT7 1NN. e-mail: amckee240@qub.ac.uk
ADAM SKALSKI
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland. e-mail: a.skalski@impan.pl
IVAN G. TODOROV
Affiliation:
Mathematical Sciences Research Centre, Queen's University Belfast, Belfast BT7 1NN. e-mail: i.todorov@qub.ac.uk
LYUDMILA TUROWSKA
Affiliation:
Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg SE-412 96, Sweden. e-mail: turowska@chalmers.se
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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.

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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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References

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