{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QQIB3VVN7RI6R2UL66P5K3WYBQ","short_pith_number":"pith:QQIB3VVN","schema_version":"1.0","canonical_sha256":"84101dd6adfc51e8ea8bf79fd56ed80c2ddbd9917ff66f6e0cafd0acc5664bf3","source":{"kind":"arxiv","id":"1802.01973","version":1},"attestation_state":"computed","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}), \\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.01973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-06T14:42:10Z","cross_cats_sorted":[],"title_canon_sha256":"8b2b2a6a6959977ea0a3b4777f5d73a52649ba828e45fa342c62724cb1657e4b","abstract_canon_sha256":"b685922bcdb2a06d92bb5bf40765c31eca4607b7b4db9162dc005fc084f303d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:20.799118Z","signature_b64":"1Z0+VI+5xt8iiWP6GrqzKJfoMJdDY1fC/Uu6BOfynIVeDYUwg77+VPVVhnpzfnSju5ZXtJ90a+AEkQa6EDFrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84101dd6adfc51e8ea8bf79fd56ed80c2ddbd9917ff66f6e0cafd0acc5664bf3","last_reissued_at":"2026-05-18T00:24:20.798699Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:20.798699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1802.01973","created_at":"2026-05-18T00:24:20.798756+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.01973v1","created_at":"2026-05-18T00:24:20.798756+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01973","created_at":"2026-05-18T00:24:20.798756+00:00"},{"alias_kind":"pith_short_12","alias_value":"QQIB3VVN7RI6","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QQIB3VVN7RI6R2UL","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QQIB3VVN","created_at":"2026-05-18T12:32:46.962924+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QQIB3VVN7RI6R2UL66P5K3WYBQ","json":"https://pith.science/pith/QQIB3VVN7RI6R2UL66P5K3WYBQ.json","graph_json":"https://pith.science/api/pith-number/QQIB3VVN7RI6R2UL66P5K3WYBQ/graph.json","events_json":"https://pith.science/api/pith-number/QQIB3VVN7RI6R2UL66P5K3WYBQ/events.json","paper":"https://pith.science/paper/QQIB3VVN"},"agent_actions":{"view_html":"https://pith.science/pith/QQIB3VVN7RI6R2UL66P5K3WYBQ","download_json":"https://pith.science/pith/QQIB3VVN7RI6R2UL66P5K3WYBQ.json","view_paper":"https://pith.science/paper/QQIB3VVN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.01973&json=true","fetch_graph":"https://pith.science/api/pith-number/QQIB3VVN7RI6R2UL66P5K3WYBQ/graph.json","fetch_events":"https://pith.science/api/pith-number/QQIB3VVN7RI6R2UL66P5K3WYBQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QQIB3VVN7RI6R2UL66P5K3WYBQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QQIB3VVN7RI6R2UL66P5K3WYBQ/action/storage_attestation","attest_author":"https://pith.science/pith/QQIB3VVN7RI6R2UL66P5K3WYBQ/action/author_attestation","sign_citation":"https://pith.science/pith/QQIB3VVN7RI6R2UL66P5K3WYBQ/action/citation_signature","submit_replication":"https://pith.science/pith/QQIB3VVN7RI6R2UL66P5K3WYBQ/action/replication_record"}},"created_at":"2026-05-18T00:24:20.798756+00:00","updated_at":"2026-05-18T00:24:20.798756+00:00"}