  Let $F$ be a finite extension of $Q_p$, $p>2$. We construct admissible
unitary completions of certain representations of $GL_2(F)$ on $L$-vector
spaces, where $L$ is a finite extension of $F$. When $F=Q_p$ using the results
of Berger, Breuil and Colmez we obtain some results about lifting 2-dimensional
mod $p$ representations of the absolute Galois group of $Q_p$ to crystabelline
representations with given Hodge-Tate weights.
