  The Emerton-Jacquet functor is a tool for studying locally analytic
representations of p-adic Lie groups. It provides a way to access the theory of
p-adic automorphic forms. Here we give an adjunction formula for the
Emerton-Jacquet functor, relating it directly to locally analytic inductions,
under a strict hypothesis that we call non-critical. We also further study the
relationship to socles of principal series in the non-critical setting.
