Geodesic
Exponential Boundedness and Amenability of Open Subsemigroupsof Locally Compact Groups
Canadian journal of mathematics, Tome 46 (1994) no. 6, pp. 1263-1274

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a connected amenable locally compact group with left Haar measure λ. In an earlier work Jenkins claimed that exponential boundedness of G is equivalent to each of the following conditions: (a) every open subsemigroup S ⊆ G is amenable; (b) given and a compact K ⊆ G with nonempty interior there exists an integer n such that (c) given a signed measure of compact support and nonnegative nonzero f ∈ L ∞(G), the condition v * f ≥ 0 implies v(G) ≥ 0. However, Jenkins‚ proof of this equivalence is not complete. We give a complete proof. The crucial part of the argument relies on the following two results: (1) an open σ-compact subsemigroup S ⊆ G is amenable if and only if there exists an absolutely continuous probability measure μ on S such that lim for every s ∈ S; (2) G is exponentially bounded if and only if for every nonempty open subset U ⊆ G.
DOI : 10.4153/CJM-1994-071-2
Mots-clés : 43A07, 22D05, 43A05, 60B15 
Jaworski, Wojciech. Exponential Boundedness and Amenability of Open Subsemigroupsof Locally Compact Groups. Canadian journal of mathematics, Tome 46 (1994) no. 6, pp. 1263-1274. doi: 10.4153/CJM-1994-071-2
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