In their paper Twice-Ramanujan sparsifiers, Batson, Spielman and Srivastava show that, given a sum of rank-one n x n matrices, one can find O(n) terms whose sum, once appropriately reweighted, has the same spectral properties as the original matrix. We prove a generalization of this result in infinite dimension, and discuss the implications in terms of discretization of L^p norms and least-squares approximation based on point samples. This is joint work with Abdellah Chkifa, David Krieg and Mario Ullrich.