arXiv subjects

Tim de Laat

Publications and source records attributed to Tim de Laat.

22 records · Page 2Linked to original sources

arXiv2013

Approximation properties for noncommutative Lp-spaces associated with lattices in Lie groups

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 < 4/3 and 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 < 12/11 and p > 12. It follows that a large class of noncommutative Lp-spaces does not have the OAP or CBAP.

math.OA↗

arXiv2013

Simple Lie groups without the Approximation Property

For a locally compact group G, let A(G) denote its Fourier algebra, and let M_0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-* topology on the space M_0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center and real rank greater than or equal to two do not have the AP. This naturally gives rise to many examples of exact discrete groups without the AP.

math.OA↗

arXiv2013

On the Grothendieck Theorem for jointly completely bounded bilinear forms

We show how the proof of the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras by Haagerup and Musat can be modified in such a way that the method of proof is essentially C*-algebraic. To this purpose, we use Cuntz algebras rather than type III factors. Furthermore, we show that the best constant in Blecher's inequality is strictly greater than one.

math.OA↗

arXiv2010

On the Regularization of the Kepler Problem

We show that for the Kepler problem the canonical Ligon-Schaaf regularization map can be understood in a straightforward manner as an adaptation of the Moser regularization. In turn this explains the hidden symmetry in a geometric way.

math.SG↗