  Let $G$ be a $p$-adic Lie group with reductive Lie algebra $\mathfrak{g}$. In
analogy to the translation functors introduced by Bernstein and Gelfand on
categories of $U(\mathfrak{g})$-modules we consider similarly defined functors
on the category of coadmissible modules over the locally analytic distribution
algebra $D(G)$ on which the center of $U(\mathfrak{g})$ acts locally finite.
These functors induce equivalences between certain subcategories of the latter
category. Furthermore, these translation functors are naturally related to
those on category $\mathcal{O}$ via the functors from category $\mathcal{O}$ to
the category of coadmissible modules. We also investigate the effect of the
translation functors on locally analytic representations $\Pi(V)^{\rm la}$
associated by the $p$-adic Langlands correspondence for ${\rm
GL}_2(\mathbb{Q}_p)$ to 2-dimensional Galois representations $V$.
