Non commutative Lp spaces without the completely bounded approximation property
Abstract
For any 1\leq p \leq \infty 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 r\geq 3 these examples are the noncommutative Lpspaces 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 noncommutative Lpspaces of the von Neumann algebra of lattices in SL_r(F) for r large enough depending on p. We also prove that if r \geq 3 lattices in SL_r(F) or SL_r(\R) do not have the Approximation Property of Haagerup and Kraus. This provides examples of exact C^*algebras without the operator space approximation property.
 Publication:

arXiv eprints
 Pub Date:
 April 2010
 arXiv:
 arXiv:1004.2327
 Bibcode:
 2010arXiv1004.2327L
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Group Theory
 EPrint:
 v3