Property (T) for locally compact groups and C*-algebras
Résumé
Let G be a locally compact group and let C∗(G) and C∗r(G) be the full group C∗-algebra and the reduced group C∗-algebra of G. We investigate the relationship between Property (T) for G and Property (T) as well as its strong version for C∗(G) and C∗r(G). We show that G has Property (T) if (and only if) C∗(G) has Property (T). In the case where G is a locally compact IN-group, we prove that G has Property (T) if and only if C∗r(G) has strong Property (T). We also show that C∗r(G) has strong Property (T) for every non-amenable locally compact group G for which C∗r(G) is nuclear. Some of these groups (as for instance G=SL2(R)) do not have Property T.
Domaines
Analyse fonctionnelle [math.FA]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...