Motivated by a hypothetical p-adic Langlands correspondence for GLn(Qp) we associate to an n-dimensional ordinary (i.e. upper-triangular) representation rho of Gal(Qp-bar/Qp) over E a unitary Banach space representation Pi(rho)^ord of GLn(Qp) over E that is built out of principal series representations. (Here, E is a finite extension of Qp.) There is an analogous construction over Fp-bar. In the latter case we show under suitable hypotheses that Pi(rho)^ord occurs in the rho-part of the cohomology of a compact unitary group. This is joint work with Christophe Breuil.