  This paper develops various foundational results in the locally analytic
representation theory of p-adic groups. In particular, we define the functor
``pass to locally analytic vectors'', which attaches to any continuous
representation of a p-adic analytic group on a locally convex p-adic
topological vector space the associated space of locally analytic vectors.
Using this functor, and the point of view that its construction suggests, we
establish some basic facts about admissible locally analytic representations
(as defined by Schneider and Teitelbaum). We also introduce the related notion
of essentially admissible locally analytic representations.
