Let H be a Hilbert space. Given a bounded positive definite
operator S on H, and a bounded sequence c={ck}k∈N of non negative real numbers, the pair (S,c) is
frame admissible, if there exists a frame {fk}k∈N on
H with frame operator S, such that ∥fk∥2=ck, k∈N. We relate the existence of such frames with the Schur-Horn
theorem of majorization, and give a reformulation of the extended version of
Schur-Horn theorem, due to A. Neumann. We use it to get necessary conditions
(and to generalize known sufficient conditions) for a pair (S,c),
to be frame admissible.Comment: To appear in Illinois Journal of Mat