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- W2215976614 abstract "C. Anantharaman-Delaroche and J. Renault have proved that the amenability of a topological locally compact groupoid implies the equality of the reduced and the full C*-algebras. In this paper we shall prove the converse assertion under a technical hypothesis. We shall prove that if G is a locally compact second countable groupoid endowed with a Haar system having ”a bounded decomposition over the principal groupoid associated to G”, then the equality C*red (G) = C* (G) implies the amenability of all quasi-invariant measures. In order to prove this we shall see that the inequality $$left| {II_mu (f)} right| leqslant left| {operatorname{Re} g_mu (f)} right|$$ for all f Є C c (G) implies a similar inequality for all f Є I (G, ν, μ) (where Regμ is the left regular representation of C c (G) on a quasi invariant measure μ, and IIμ is the trivial representation on μ)." @default.
- W2215976614 created "2016-06-24" @default.
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- W2215976614 date "2004-01-01" @default.
- W2215976614 modified "2023-09-27" @default.
- W2215976614 title "The Equality of the Reduced and the Full C*-Algebras and the Amenability of a Topological Groupoid" @default.
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- W2215976614 doi "https://doi.org/10.1007/3-7643-7314-8_4" @default.
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