{"paper":{"title":"Weighted Procrustes problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alejandra Maestripieri, Juan Giribet, Maximiliano Contino","submitted_at":"2016-10-03T14:00:30Z","abstract_excerpt":"Let $\\mathcal{H}$ be a Hilbert space, $L(\\mathcal{H})$ the algebra of bounded linear operators on $\\mathcal{H}$ and $W \\in L(\\mathcal{H})$ a positive operator such that $W^{1/2}$ is in the p-Schatten class, for some $1 \\leq p< \\infty.$ Given $A \\in L(\\mathcal{H})$ with closed range and $B \\in L(\\mathcal{H}),$ we study the following weighted approximation problem: analize the existence of $$\\underset{X \\in L(\\mathcal{H})}{min}\\Vert AX-B \\Vert_{p,W},$$ where $\\Vert X \\Vert_{p,W}=\\Vert W^{1/2}X \\Vert_{p}.$\n  In this paper we prove that the existence of this minimum is equivalent to a compatibilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00558","kind":"arxiv","version":1},"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"}