Existence de normes invariantes pour GL2

In [8] Breuil and Schneider (2007) stated a conjecture on the equivalence between the existence of invariant norms on certain locally algebraic representations of GLd(F) and the existence of certain de Rham representations of Gal(Q¯p/F), where F is a finite extension of Qp. In this paper we prove that in the case d=2 and under some conditions, the existence of certain admissible filtrations implies the existence of invariant norms.