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$^*$ in $B_2(\Gamma)$ i.e $w(\phi_i) \to w(1)$ for every $w \in Q(\Gamma)$.

A wanted to know, if anything is known in the literature about the Thompson's group $V$, having property-AP?

It would be great, if I am directed to some research papers regarding the same.

Thanks for the help!!