Approximation properties of fine hyperbolic graphs (Q282321)

For a countable discrete group \(G\), some approximation properties of the reduced \(C^*\)-algebra \(C^*_r(G)\) give approximation properties of \(G\). A definition of the approximation property to be called the metric invariant translation approximation property for a discrete countable metric space is proposed and it is shown that a fine hyperbolic graph has the metric invariant translation approximation property.