  The p-adic local Langlands correspondence for GL_2(Q_p) is given by an exact
functor from unitary Banach representations of GL_2(Q_p) to representations of
the absolute Galois group G_{Q_p} of Q_p. We prove, using characteristic 0
methods, that this correspondence induces a bijection between absolutely
irreducible non-ordinary representations of GL_2(Q_p) and absolutely
irreducible 2-dimensional representations of G_{Q_p}. This had already been
proved, by characteristic p methods, but only for p\geq 5.
