1 October 2011 Noncommutative Lp-spaces without the completely bounded approximation property
Vincent Lafforgue, Mikael De la Salle
Duke Math. J. 160(1): 71-116 (1 October 2011). DOI: 10.1215/00127094-1443478

Abstract

For any 1p different from 2, we give examples of noncommutative Lp-spaces without the completely bounded approximation property. Let F be a nonarchimedian local field. If p>4 or p<4/3 and r3 these examples are the noncommutative Lp-spaces of the von Neumann algebra of lattices in SLr(F) or in SLr(R). For other values of p the examples are the noncommutative Lp-spaces of the von Neumann algebra of lattices in SLr(F) for r large enough depending on p.

We also prove that if r3 lattices in SLr(F) or SLr(R) do not have the approximation property of Haagerup and Kraus. This provides examples of exact C-algebras without the operator space approximation property.

Citation

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Vincent Lafforgue. Mikael De la Salle. "Noncommutative Lp-spaces without the completely bounded approximation property." Duke Math. J. 160 (1) 71 - 116, 1 October 2011. https://doi.org/10.1215/00127094-1443478

Information

Published: 1 October 2011
First available in Project Euclid: 27 September 2011

zbMATH: 1267.46072
MathSciNet: MR2838352
Digital Object Identifier: 10.1215/00127094-1443478

Subjects:
Primary: 46L07
Secondary: 22D25 , 46B28

Rights: Copyright © 2011 Duke University Press

Vol.160 • No. 1 • 1 October 2011
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