  Given a compact p-adic Lie group G over a finite unramified extension L/Q_p
let G_0 be the product over all Galois conjugates of G. We construct an exact
and faithful functor from admissible G-Banach space representations to
admissible locally L-analytic G_0-representations that coincides with passage
to analytic vectors in case L=Q_p. On the other hand, we study the functor
"passage to analytic vectors" and its derived functors over general basefields.
As an application we determine the higher analytic vectors in certain locally
analytic induced representations.
