  The p-adic local Langlands correspondence for GL2(Qp) attaches to any
2-dimensional irreducible p-adic representation V of the absolute Galois groups
of Qp an admissible unitary representation Pi(V) of GL2(Qp). The unitary
principal series of GL2(Qp) are those Pi(V) corresponding to trianguline
representations. In this article, for p>2, using the machinery of Colmez, we
determine the space of locally analytic vectors for all non-exceptional unitary
principal series of GL2(Qp) by proving a conjecture of Emerton.
