  We prove some qualitative results about the $p$-adic Jacquet--Langlands
correspondence defined by Scholze, in the $GL(2,Q_p)$, residually reducible
case, by using a vanishing theorem proved by Judith Ludwig. In particular, we
show that in the cases under consideration the $p$-adic Jacquet--Langlands
correspondence can also deal with principal series representations in a
non-trivial way, unlike its classical counterpart.
