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Amenability and Co-Amenability for Locally Compact Quantum Groups
International Journal of Mathematics, 2003We define concepts of amenability and co-amenability for locally compact quantum groups in the sense of J. Kustermans and S. Vaes. Co-amenability of a lcqg (locally compact quantum group) is proved to be equivalent to a series of statements, all of which imply amenability of the dual lcqg.
Bédos, E., Tuset, L.
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Countable Amenable Identity Excluding Groups
Canadian Mathematical Bulletin, 2004AbstractA discrete group G is called identity excluding if the only irreducible unitary representation of G which weakly contains the 1-dimensional identity representation is the 1-dimensional identity representation itself. Given a unitary representation π of G and a probability measure μ on G, let Pμ denote the μ-average ∫π(g)μ(dg).
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Chracters on Weighted Amenable Groups
Bulletin of the London Mathematical Society, 1991Let \(G\) be a locally compact group. A crucial lemma in this article, of Hahn-Banach type, shows that if \(G\) is amenable and equipped with a weight, i.e., a measurable submultiplicative positive function \(\omega\) on \(G\), existence of an invariant mean on \(L^ \infty(G)\) implies existence of a continuous positive character \(\Phi\) on \(G\) such
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Weak Amenability of Group Algebras
Bulletin of the London Mathematical Society, 1991This paper provides a proof that if \(G\) is a locally compact group then the algebra \(L^ 1(G)\) is weakly amenable, that is any derivation from \(L^ 1(G)\) to \(L^ \infty(G)\) is inner.
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Amenability and Right Orderable Groups
Bulletin of the London Mathematical Society, 1993Let \(G\) be a group that is supramenable, i.e., it has no paradoxical subsets. Assume it is right ordered, i.e., it admits a total ordering \(\leq\) such that \(x \leq y \Rightarrow xz \leq yz\) whenever \(x, y, z \in G\). The structure of these groups is described via the Banach-Tarski paradox. Moreover, amenable groups admitting a homomorphism into \
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