Assume that $\phi$ is a Fubini-Study metric. If $L$ is very ample, then $\widehat{V}_{{\scriptscriptstyle\bullet}}(L,\phi)$, $\widehat{V}(L_{X|Y},\phi_{X|Y})$ and $\widehat{V}_{{\scriptscriptstyle\bullet}}(L|_{Y},\phi|_{Y})$ are affinoid algebras.