In this paper, we introduce actions of fusion algebras on unital $$C^*$$ -algebras, and define amenability for algebraic actions. Motivated by S. Neshveyev et al.’s work, considering the representation ring a compact quantum group as algebra, canonical (for short, CFA) form discrete action space. Furthermore, through CFA form, FA-amenability actions, present some basic connections between FA-am...

We study actions of discrete groups on Hilbert C-modules induced from topological actions on compact Hausdorff spaces. We prove that amenable actions give rise to proper affine isometric actions, provided there is a quasiinvariant measure which is sufficiently close to being invariant in a certain sense. This provides conditions on non-amenability of actions. The notion of amenability of group ...

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...

In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra B(E) of all bounded linear operators on a Banach space E could ever be amenable if dimE = ∞. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros– Haydon result that solves the “scalar plus compact problem”: there is a...

It is well-known that a Kleinian group is amenable if and only if it is elementary. We establish an analogous property for equivalence relations and foliations with Gromov hyperbolic leaves: they are amenable if and only if they are elementary in the sense that one can assign (in a measurable way) to any leaf a finite subset of its hyperbolic boundary (as in the group case, such subsets cannot ...

Novel diagnostic tests hold promise for improving tuberculosis (TB) control, but their epidemiologic impact remains uncertain. Using data from the World Health Organization (2011-2012), we developed a transmission model to evaluate the deployment of 3 hypothetical TB diagnostic tests in Southeast Asia under idealized scenarios of implementation. We defined diagnostics by their sensitivity for s...

Let (G,S) be a Coxeter group. We construct a continuation, to the open unit disc, of the unitary representations associated to the positive definite functions g 7→ rl(g). (Here 0 < r < 1, and l denotes the length function with respect to the generating set S.) The constructed representations are uniformly bounded and we prove that this implies the weak amenability of the group G. Résumé Soit (G...

In a previous paper the authors developed an operator-algebraic approach to Lewis Bowen’s sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by measure-preserving transformations on a standard probability space. We show here that these measure and topological entropy invariants both coincide with their classical...

We prove that hyperbolic groups are weakly amenable. This partially extends the result of Cowling and Haagerup showing that lattices in simple Lie groups of real rank one are weakly amenable. We take a combinatorial approach in the spirit of Haagerup and prove that for the word length metric d on a hyperbolic group, the Schur multipliers associated with r have uniformly bounded norms for 0 < r ...