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Amenability properties of unitary co-representations of locally compact quantum groups. (English) Zbl 1430.22005
The authors introduce a notion of strong amenability for a unitary co-representation \(U\) of a locally compact quantum group \(G\) on a Hilbert space \(H_{U}\). They show that this notion is stronger than the strong amenability of \(G.\) Also they give a quantum version of the Lau-Paterson result. Applying this result, they show that \(W_{G}\) is strongly amenable if and only if \(G\) is strongly amenable.
MSC:
22D10 Unitary representations of locally compact groups
43A07 Means on groups, semigroups, etc.; amenable groups
43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
46L10 General theory of von Neumann algebras
46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory
47C15 Linear operators in \(C^*\)- or von Neumann algebras
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