{"paper":{"title":"Shorted operators and minus order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alejandra Maestripieri, Juan Ignacio Giribet, Maximiliano Contino","submitted_at":"2018-02-06T14:42:10Z","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. Given a closed subspace $\\mathcal{S}$ of $\\mathcal{H}$, we characterize the shorted operator $W_{/ \\mathcal{S}}$ of $W$ to $\\mathcal{S}$ as the maximum and as the infimum of certain sets, for the minus order $\\stackrel{-}{\\leq}.$ Also, given $A \\in L(\\mathcal{H})$ with closed range, we study the following operator approximation problem considering the minus order: $$ min_{\\stackrel{-}{\\leq}} \\ \\{(AX-I)^*W(AX-I) : X \\in L(\\mathcal{H}), \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01973","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"}