Existence de normes invariantes pour GL_2
  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. 
Marco De Ieso
math.RT