1. Amenability of locally compact quantum groups and their unitary co-representations
- Author
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Ng, Chi-Keung and Viselter, Ami
- Subjects
Mathematics - Functional Analysis ,20G42 (Primary), 22D25, 46L89 (Secondary) ,Mathematics::Operator Algebras ,Mathematics - Operator Algebras ,FOS: Mathematics ,Operator Algebras (math.OA) ,Functional Analysis (math.FA) - Abstract
We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of B\'edos, Conti and Tuset. As a corollary, we extend to locally compact quantum groups a result of the first-named author, which characterizes amenability of a locally compact group $G$ by nuclearity of the reduced group $C^{*}$-algebra $C_{r}^{*}(G)$ and an additional condition., Comment: 9 pages; a new co-author; added to Theorem 3.2 a second part about the case of a trivial scaling group, and gave an alternative proof of one of the implications; to appear in the Bulletin of the London Mathematical Society
- Published
- 2016
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