  Let $\mathcal H$ be a Hilbert space. Given a bounded positive definite
operator $S$ on $\mathcal H$, and a bounded sequence $\mathbf{c} = \{c_k \}_{k
\in \mathbb N}$ of non negative real numbers, the pair $(S, \mathbf{c})$ is
frame admissible, if there exists a frame $\{f_k \}_{k \in \mathbb{N}} $ on
$\mathcal H$ with frame operator $S$, such that $\|f_k \|^2 = c_k$, $k \in
\mathbb {N}$. 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 $(S, \mathbf{c})$,
to be frame admissible.
