  Let L be a finite extension of Qp, and let K be a spherically complete
non-archimedean extension field of L. In this paper we introduce a restricted
category of continuous representations of locally L-analytic groups G in
locally convex K-vector spaces. We call the objects of this category
"admissible" representations and we establish some of their basic properties.
Most importantly we show that (at least when G is compact) the category of
admissible representations in our sense can be algebraized; it is faithfully
full (anti)-embedded into the category of modules over the locally analytic
distribution algebra D(G,K) of G over K.
  As an application of our theory, we prove the topological irreducibility of
generic members of the p-adic principal series of GL(2,Qp).
