Continuity of the dual Haar measure
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.
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-05-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.183/ |
| Summary: | 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. |
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| ISSN: | 1778-3569 |