In 2010, Lafforgue and de la Salle gave examples of noncommutative Lp-spaces
without the operator space approximation property (OAP) and, hence, without the
completely bounded approximation property (CBAP). To this purpose, they
introduced the property of completely bounded approximation by Schur
multipliers on Sp and proved that for p 4 the groups SL(n,Z),
with n \geq 3, do not have it. Since for 1 < p < \infty the property of
completely bounded approximation by Schur multipliers on Sp is weaker than the
approximation property of Haagerup and Kraus (AP), these groups were also the
first examples of exact groups without the AP. Recently, Haagerup and the
author proved that also the group Sp(2,R) does not have the AP, without using
the property of completely bounded approximation by Schur multipliers on Sp. In
this paper, we prove that Sp(2,R) does not have the property of completely
bounded approximation by Schur multipliers on Sp for p 12. It
follows that a large class of noncommutative Lp-spaces does not have the OAP or
CBAP.Comment: Version 2, 20 pages. Minor corrections, builds on results from
arXiv:1201.125
