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Positive Herz-Schur multipliers and approximation properties of crossed products
- Publication Year :
- 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 $K(\ell^2(X))\otimes A$. We then relate them to completely positive Herz-Schur multipliers on $C^*$-algebraic crossed products of the form $A\rtimes_{\alpha,r} G$, with $G$ a discrete group, whose various versions were considered earlier by Anantharaman-Delaroche, B\'edos and Conti, and Dong and Ruan. The latter maps are shown to implement approximation properties, such as nuclearity or the Haagerup property, for $A\rtimes_{\alpha,r} G$.<br />Comment: 21 pages, v2 corrects a few minor typos. The paper will appear in the Mathematical Proceedings of the Cambridge Philosophical Society
- Subjects :
- Mathematics - Operator Algebras
Primary: 46L55, Secondary: 43A35, 46L05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1705.03300
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1017/S0305004117000639