  Breuil et Schneider formulated a conjecture on the equivalence of the
existence of invariant norms on certain locally algebraic representations of
GL_d(F) and the existence of certain de Rham representations of
Gal(\bar(Q_p)/F)$, where F is a finite extension of Q_p. In this paper we prove
that in the case d = 2 and under some conditions, the existence of certains
admissible filtrations implies the existence of invariant norms.

Representation Theory