{"paper":{"title":"Frames of subspaces and operators","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Demetrio Stojanoff, Mariano A. Ruiz","submitted_at":"2007-06-11T14:30:40Z","abstract_excerpt":"We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces $\\mathcal{E} = \\{E_i \\}_{i\\in I}$ of a Hilbert space $\\mathcal{K}$ and a surjective $T\\in L(\\mathcal{K}, \\mathcal{H})$ in order that $\\{T(E_i)\\}_{i\\in I}$ is a frame of subspaces with respect to a computable sequence of weights. We also obtain generalizations of results in [J. A. Antezana, G. Corach, M. Ruiz and D. Stojanoff, Oblique projections and frames. P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.1484","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":""},"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"}