2005/08/31 by Jorge Antezana, J. Antezana, Antezana, J. +9 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Primary 42C15 #Secondary 47A05 #Spectral Theory in Mathematical Physics #math.FA #msc:42C15 #msc:47A05
paper · pdf · doi:10.48550/arxiv.math/0508646
To appear in Illinois Journal of Math
openalex publication_date 2005/08/31 · arxiv created 2005/09/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathcal H be a Hilbert space. Given a bounded positive definite operator S on \mathcal H, and a bounded sequence c = \ck \k ∈ \mathbb N of non negative real numbers, the pair (S, c) is frame admissible, if there exists a frame \fk \k ∈ ℕ on \mathcal H with frame operator S, such that ‖fk ‖2 = ck, k ∈ \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, c), to be frame admissible.