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Comptes Rendus. Mathématique
Functional analysis, Harmonic analysis
Continuity of the dual Haar measure
Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 415-419.

Given a continuous field of locally compact groups, we show that the field of the Plancherel weights of their C*-algebras is lower semi-continuous. As a corollary, we obtain that the dual Haar system of a continuous Haar system of a locally compact abelian group bundle is also continuous.

Étant donné un champ continu de groupes localement compacts, on montre que le champ des poids de Plancherel de leurs C*-algèbres est semi-continu inférieurement. On en déduit que, lorsque les groupes sont abéliens, le système de Haar dual d’un système de Haar continu est aussi continu.

Received:
Accepted:
Published online:
DOI: https://doi.org/10.5802/crmath.183
Jean Renault 1

1. Institut Denis Poisson (UMR 7013) Université d’Orléans et CNRS, 45067 Orléans Cedex 2, France.
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Jean Renault. Continuity of the dual Haar measure. Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 415-419. doi : 10.5802/crmath.183. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.183/

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