Comptes Rendus
no. 7
Functional analysis
On connected Lie groups and the approximation property
[Sur les groupes de Lie connexes et la propriété d'approximation]

Présenté par : Gilles Pisier

Søren Knudby1
1 Mathematical Institute, University of Münster, Einsteinstraße 62, 48149 Münster, Germany
Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 697-699.

Une caractérisation complète des groupes de Lie connexes avec la propriété d'approximation a été obtenue récemment. La preuve utilisait la propriété (T⁎), nouvellement introduite. Nous présentons ici une preuve courte du même résultat sans utiliser la propriété (T⁎). En utilisant (T⁎), cependant, la caractérisation est étendue aux groupes localement compacts presque connexes. Nous concluons avec quelques remarques sur la difficulté d'aller au-delà du cas presque connexe.

Recently, a complete characterization of connected Lie groups with the Approximation Property was given. The proof used the newly introduced property (T⁎). We present here a short proof of the same result avoiding the use of property (T⁎). Using property (T⁎), however, the characterization is extended to almost connected locally compact groups. We end with some remarks about the difficulty of going beyond the almost connected case.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2016.04.007
Søren Knudby 1

1 Mathematical Institute, University of Münster, Einsteinstraße 62, 48149 Münster, Germany 
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Søren Knudby. On connected Lie groups and the approximation property. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 697-699. doi : 10.1016/j.crma.2016.04.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.04.007/

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