Let F and E be two finite extensions of Qp such that E is large enough. Let r : Gal(F_bar/F) -> GL_n(E) be a Galois representation. In 2013 Caraiani, Emerton, Gee, Geraghty, Paskunas and Shin have constructed an E -Banach representation V(r) of GL_n(F). The authors have hypothesized that the representation V(r) corresponds to Galois representation r under hypothetical p-adic Langlands correspondence. In this work, we show that, under certain assumptions on r, the locally algebraic vectors of V(r) are isomorphic to an irreducible locally algebraic representation. This locally algebraic representation can be determined explicitly via the classical local Langlands correspondence and the knowledge of the Hodge-Tate weights of the Galois representation. From this we can derive new cases of the Breuil-Schneider conjecture.