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Property AP: A discrete group $\Gamma$ has property AP (Approximation Property) if there exists a net $(\phi_i)_{i \in I}$ of finitely supported functions on $\Gamma$ such that $\phi_i \to 1 $ weak$^*$...

Consider the free product of $\mathbb{Z}/2$ with itself with generators $$ \mathbb{Z}/2*\mathbb{Z}/2=\langle u,v\mid u^2=1=v^2\rangle $$ and regard its group $C^*$-algebra $$ C^*(\mathbb{Z}/2*\mathbb{...

Suppose $A$ and $B$ are two countable, discrete, amenable groups. One definition of amenability tells us that there is a sequence of finitely supported, positive definite functions that converges to 1 ...