Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-21T01:19:50.955Z Has data issue: false hasContentIssue false
  • English
  • Français

On Godement's characterisation of amenability

Published online by Cambridge University Press:  17 April 2009

Alain Valette
Alain Valette
Affiliation:
Institut de MathématiquesRue Emile Argand 11CH-2007NeuchâtelSwitzerland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Motivated by a question related to the construction of the Baum-Connes analytical assembly map for locally compact groups, we refine a criterion of Godement for amenability: for a unimodular group G, our criterion says that G is amenable if and only if every compactly supported, positive-definite function has non-negative integral over G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 153 - 158
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Berg, C. and Christensen, P.R., ‘On the relation between amenability of locally compact groups and the norms of convolution operators’, Math. Ann, 208 (1974), 148–153.CrossRefGoogle Scholar
[2]Baum, P., Connes, A. and Higson, N., ‘Classifying spaces for proper actions and K-theory of group C*-algebras’, in C*-algebras 1943–1993, a fifty year celebration (Contemporary Mathematics 167, 1994), pp. 241–291.Google Scholar
[3]Connes, A., Noncommutatiue geometry (Academic Press, San Diego, 1994).Google Scholar
[4]Derriennic, Y. and Guivarc'h, Y., ‘Théorème de renouvellement pour les groupes non moyennables’, C.R. Acad. Sci. Paris 277 (1973), 613–615.Google Scholar
[5]Dixmier, J., C*-algebras (North Holland, Amsterdam, New York, 1977).Google Scholar
[6]Ferry, S.C., Ranicki, A. and Rosenberg, J., ‘A history and survey of the Novikov conjecture’, in Novikov conjectures, index theorems and rigidity, London Math. Society Lecture Notes Series 226 (Cambridge University Press, Cambridge, 1995), pp. 7–66.CrossRefGoogle Scholar
[7]Godement, R., ‘Les fonctions de type positif et la théorie des groupes’, Trans. Amer. Math. Soc. 63 (1948), 1–84.Google Scholar
[8]Julg, P., ‘Remarks on the Baum-Connes conjecture and Kazhdan's property T’, Fields Institute Communciations 13 (1997), 145–153.Google Scholar
[9]Kesten, H., ‘Symmetric random walks on groups’, Trans. Amer. Math. Soc. 92 (1959), 336–354.CrossRefGoogle Scholar
[10]Jensen, K. and Thomsen, K., Elements of KK-theory (Birkhäuser, Boston, Basel, 1991).CrossRefGoogle Scholar
[11]Palais, R., ‘On the existence of slices for actions of non-compact Lie groups’, Ann. of Math. 73 (1961), 295–323.CrossRefGoogle Scholar
[12]Pier, J-P., Amenable locally compact groups (Wiley–Interscience, New York, 1984).Google Scholar
[13]Valette, A., ‘On the Baum-Connes assembly map for discrete groups’, (preprint, 1997).Google Scholar