# Noncommutative $L^{p}$-spaces without the completely bounded approximation property

@article{Lafforgue2011NoncommutativeW,
title={Noncommutative \$L^\{p\}\$-spaces without the completely bounded approximation property},
author={V. Lafforgue and M. D. L. Salle},
journal={Duke Mathematical Journal},
year={2011},
volume={160},
pages={71-116}
}
• Published 2011
• Mathematics
• Duke Mathematical Journal
• For any 1\leq p \leq \infty different from 2, we give examples of non-commutative Lp spaces without the completely bounded approximation property. Let F be a non-archimedian local field. If p>4 or p<4/3 and r\geq 3 these examples are the non-commutative Lp-spaces of the von Neumann algebra of lattices in SL_r(F) or in SL_r(\R). For other values of p the examples are the non-commutative Lp-spaces of the von Neumann algebra of lattices in SL_r(F) for r large enough depending on p. We also prove… CONTINUE READING
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