Analytic vectors in continuous p-adic representations

Given a compact p-adic Lie group G over a finite unramified extension L/Q(p) let G(L/Qp), 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(L/Qp) -representations that coincides with passage to analytic vectors in the 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 compute the higher analytic vectors in certain locally analytic induced representations.