{"paper":{"title":"The Schur-Horn theorem for operators and frames with prescribed norms and frame operator","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D.Stojanoff, J. Antezana, M.Ruiz, P. Massey","submitted_at":"2005-08-31T17:12:32Z","abstract_excerpt":"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 conditi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508646","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0508646/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}