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Title: Approximation properties for noncommutative Lp-spaces associated with lattices in Lie groups
Authors: de Laat, Tim # ×
Issue Date: 15-May-2013
Publisher: Academic Press
Series Title: Journal of Functional Analysis vol:264 issue:10 pages:2300-2322
Abstract: In 2010, Lafforgue and de la Salle gave examples of noncommutative L^p-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 S^p and proved that for p in [1,4/3) or in (4,infinity], the groups SL(n,Z), with n > 2, do not have this property. Since for p in (1, infinity), the property of completely bounded approximation by Schur multipliers on S^p 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 S^p. In this paper, we prove that Sp(2,R) does not have the property of completely bounded approximation by Schur multipliers on S^p for p in [1,12/11) or in (12,infinity]. It follows that a large class of noncommutative L^p-spaces does not have the OAP or CBAP.
ISSN: 0022-1236
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Non-KU Leuven Association publications
× corresponding author
# (joint) last author

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