  In this paper we continue the study of locally analytic representations of a
$p$-adic Lie group $G$ in vector spaces over a spherically complete
non-archimedean field $K$, building on the algebraic approach to such
representations introduced in our paper "Locally analytic distributions and
p-adic representation theory, with applications to GL_2." In that paper we
associated to a representation $V$ a module $M$ over the ring $D(G,K)$ of
locally analytic distributions on $G$ and described an admissibility condition
on $V$ in terms of algebraic properties of $M$.
  In this paper we determine the relationship between our admissibility
condition on locally analytic modules and the traditional admissibility of
Langlands theory. We then analyze the class of locally analytic representations
with the property that their associated modules are annihilated by an ideal of
finite codimension in the universal enveloping algebra of G, showing under some
hypotheses on G that they are sums of representations of the form $X\otimes Y$,
with X finite dimensional and Y smooth. The irreducible representations of this
type are obtained when X and Y are irreducible.
  We conclude by analyzing the reducible members of the locally analytic
principal series of $SL_2(\Qp)$.
