  Let $H$ be a uniform pro-$p$ group. Associated to $H$ are rigid analytic
affinoid groups $\bbH_n$, and their "wide open" subgroups $\bbH_n^{\circ}$.
Denote by $D^\la(H)= C^\la(H)'_b$ the locally analytic distribution algebra of
$H$ and by $\DHnn$ Emerton's ring of $\bbH_n^{\circ}$-rigid analytic
distributions on $H$. If $V$ is an admissible locally analytic representation
of $H$, and if $V_{\bbH_n^\circ-\an}$ denotes the subspace of
$\bbH_n^\circ$-rigid analytic vectors (with its intrinsic topology), then we
show that the continuous dual of $V_{\bbH_n^\circ-\an}$ is canonically
isomorphic to $\DHnn \ot_{D^\la(H)} V'$. From this we deduce the exactness of
the functor $V \rightsquigarrow V_{\bbH_n^\circ-\an}$ on the category of
admissible locally analytic representations of $H$.
