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

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dc.creatorAntezana, J.
dc.creatorMassey, P.
dc.creatorRuiz, M.
dc.creatorStojanoff, D.
dc.date2005-08-31
dc.date2005-09-02
dc.date.accessioned2026-07-07T05:22:51Z
dc.date.available2026-07-07T05:22:51Z
dc.descriptionLet $\mathcal H$ 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.
dc.descriptionTo appear in Illinois Journal of Math
dc.identifierhttps://arxiv.org/abs/math/0508646
dc.identifierhttp://arxiv.org/abs/math/0508646
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76221
dc.subjectFunctional Analysis
dc.subjectPrimary 42C15, Secondary 47A05
dc.titleThe Schur-Horn theorem for operators and frames with prescribed norms and frame operator
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