{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:LKTR23GNJKGSXCX67AN5MPWS6Y","short_pith_number":"pith:LKTR23GN","schema_version":"1.0","canonical_sha256":"5aa71d6ccd4a8d2b8afef81bd63ed2f611e9c7863657e156ea1f169a6370c6b4","source":{"kind":"arxiv","id":"1905.04078","version":1},"attestation_state":"computed","paper":{"title":"Birkhoff--James orthogonality of operators in semi-Hilbertian spaces and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ali Zamani","submitted_at":"2019-05-10T11:35:06Z","abstract_excerpt":"In this paper, the concept of Birkhoff--James orthogonality of operators on a Hilbert space is generalized when a semi-inner product is considered. More precisely, for linear operators $T$ and $S$ on a complex Hilbert space $\\mathcal{H}$, a new relation $T\\perp^B_A S$ is defined if $T$ and $S$ are bounded with respect to the seminorm induced by a positive operator $A$ satisfying ${\\|T + \\gamma S\\|}_A\\geq {\\|T\\|}_A$ for all $\\gamma \\in \\mathbb{C}$. We extend a theorem due to R. Bhatia and P. \\v{S}emrl, by proving that $T\\perp^B_A S$ if and only if there exists a sequence of $A$-unit vectors $\\{"},"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":"1905.04078","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-10T11:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"7f5b16f13fdb7a0cd5e32d78a77207ad4017de6def9ccf9b1c4cacc2b981c6e6","abstract_canon_sha256":"a47cbb7e407c6e93c274a23588877132938b227877e9a087162ea9c56a1bf6e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:34.651360Z","signature_b64":"h3Q2fwI/DvT1bHguxUo53x4ahVXHa7Q7EdG38zdi0bSd1iXP+3TC6/26W8dUtgMHrqSQmHLCUgHpO7Me7xrGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5aa71d6ccd4a8d2b8afef81bd63ed2f611e9c7863657e156ea1f169a6370c6b4","last_reissued_at":"2026-05-17T23:46:34.650650Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:34.650650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Birkhoff--James orthogonality of operators in semi-Hilbertian spaces and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ali Zamani","submitted_at":"2019-05-10T11:35:06Z","abstract_excerpt":"In this paper, the concept of Birkhoff--James orthogonality of operators on a Hilbert space is generalized when a semi-inner product is considered. More precisely, for linear operators $T$ and $S$ on a complex Hilbert space $\\mathcal{H}$, a new relation $T\\perp^B_A S$ is defined if $T$ and $S$ are bounded with respect to the seminorm induced by a positive operator $A$ satisfying ${\\|T + \\gamma S\\|}_A\\geq {\\|T\\|}_A$ for all $\\gamma \\in \\mathbb{C}$. We extend a theorem due to R. Bhatia and P. \\v{S}emrl, by proving that $T\\perp^B_A S$ if and only if there exists a sequence of $A$-unit vectors $\\{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04078","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":"1905.04078","created_at":"2026-05-17T23:46:34.650812+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.04078v1","created_at":"2026-05-17T23:46:34.650812+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04078","created_at":"2026-05-17T23:46:34.650812+00:00"},{"alias_kind":"pith_short_12","alias_value":"LKTR23GNJKGS","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"LKTR23GNJKGSXCX6","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"LKTR23GN","created_at":"2026-05-18T12:33:21.387695+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/LKTR23GNJKGSXCX67AN5MPWS6Y","json":"https://pith.science/pith/LKTR23GNJKGSXCX67AN5MPWS6Y.json","graph_json":"https://pith.science/api/pith-number/LKTR23GNJKGSXCX67AN5MPWS6Y/graph.json","events_json":"https://pith.science/api/pith-number/LKTR23GNJKGSXCX67AN5MPWS6Y/events.json","paper":"https://pith.science/paper/LKTR23GN"},"agent_actions":{"view_html":"https://pith.science/pith/LKTR23GNJKGSXCX67AN5MPWS6Y","download_json":"https://pith.science/pith/LKTR23GNJKGSXCX67AN5MPWS6Y.json","view_paper":"https://pith.science/paper/LKTR23GN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.04078&json=true","fetch_graph":"https://pith.science/api/pith-number/LKTR23GNJKGSXCX67AN5MPWS6Y/graph.json","fetch_events":"https://pith.science/api/pith-number/LKTR23GNJKGSXCX67AN5MPWS6Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LKTR23GNJKGSXCX67AN5MPWS6Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LKTR23GNJKGSXCX67AN5MPWS6Y/action/storage_attestation","attest_author":"https://pith.science/pith/LKTR23GNJKGSXCX67AN5MPWS6Y/action/author_attestation","sign_citation":"https://pith.science/pith/LKTR23GNJKGSXCX67AN5MPWS6Y/action/citation_signature","submit_replication":"https://pith.science/pith/LKTR23GNJKGSXCX67AN5MPWS6Y/action/replication_record"}},"created_at":"2026-05-17T23:46:34.650812+00:00","updated_at":"2026-05-17T23:46:34.650812+00:00"}