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1 April 2013 Simple Lie groups without the approximation property
Uffe Haagerup, Tim de Laat
Duke Math. J. 162(5): 925-964 (1 April 2013). DOI: 10.1215/00127094-2087672

Abstract

For a locally compact group G, let A(G) denote its Fourier algebra, and let M0A(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 M0A(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.

Citation

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Uffe Haagerup. Tim de Laat. "Simple Lie groups without the approximation property." Duke Math. J. 162 (5) 925 - 964, 1 April 2013. https://doi.org/10.1215/00127094-2087672

Information

Published: 1 April 2013
First available in Project Euclid: 29 March 2013

zbMATH: 1266.22008
MathSciNet: MR3047470
Digital Object Identifier: 10.1215/00127094-2087672

Subjects:
Primary: 22D25
Secondary: 46B28, 46L07

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 5 • 1 April 2013
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