The Schur-Horn theorem for operators and frames with prescribed norms and frame operator

P. MASSEY; M. RUIZ; D. STOJANOFF; J. ANTEZANA

ILLINOIS JOURNAL OF MATHEMATICS

UNIV ILLINOIS URBANA-CHAMPAIGN

Año: 2007 p. 537 - 560

0019-2082

Let H be a Hilbert space. Given a bounded positive definite operator S on H, and a bounded sequence {c} = {ck }kÎ N of non negative real numbers, the pair (S,{c}) is frame admissible, if there exists a frame {fk }kÎ N on H with frame operator S, such that |f_k |2 = c_k, k Î 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.