{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GJANAECRSTWO7KRKSVCXACATNE","short_pith_number":"pith:GJANAECR","schema_version":"1.0","canonical_sha256":"3240d0105194ecefaa2a9545700813691b61419371776afbaac276dc06cec7ae","source":{"kind":"arxiv","id":"1405.1517","version":1},"attestation_state":"computed","paper":{"title":"Some Operator Bounds Employing Complex Interpolation Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.FA","authors_text":"Fedor Sukochev, Fritz Gesztesy, Yuri Latushkin, Yuri Tomilov","submitted_at":"2014-05-07T06:45:15Z","abstract_excerpt":"We revisit and extend known bounds on operator-valued functions of the type $$ T_1^{-z} S T_2^{-1+z}, \\quad z \\in \\ol \\Sigma = \\{z\\in\\bbC\\,|\\, \\Re(z) \\in [0,1]\\}, $$ under various hypotheses on the linear operators $S$ and $T_j$, $j=1,2$. We particularly single out the case of self-adjoint and sectorial operators $T_j$ in some separable complex Hilbert space $\\cH_j$, $j=1,2$, and suppose that $S$ (resp., $S^*$) is a densely defined closed operator mapping $\\dom(S) \\subseteq \\cH_1$ into $\\cH_2$ (resp., $\\dom(S^*) \\subseteq \\cH_2$ into $\\cH_1$), relatively bounded with respect to $T_1$ (resp., $"},"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":"1405.1517","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-07T06:45:15Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"48990179388eb331c4d39625dfac531acbe74c3da1c53a2c1431613bb96e9d8f","abstract_canon_sha256":"b12010f0f90600501f0db2a8618d1512421391e80efdae8ebed791b0168116de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:24.624570Z","signature_b64":"oxZguo99YVsRtV+SjC5T1JKEttet3Yo7We3GiF2uxNkRq0bg+f99FK/G0M4ZaMTrgVqct8uvRuzg2u136lq+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3240d0105194ecefaa2a9545700813691b61419371776afbaac276dc06cec7ae","last_reissued_at":"2026-05-18T02:52:24.623920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:24.623920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Operator Bounds Employing Complex Interpolation Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.FA","authors_text":"Fedor Sukochev, Fritz Gesztesy, Yuri Latushkin, Yuri Tomilov","submitted_at":"2014-05-07T06:45:15Z","abstract_excerpt":"We revisit and extend known bounds on operator-valued functions of the type $$ T_1^{-z} S T_2^{-1+z}, \\quad z \\in \\ol \\Sigma = \\{z\\in\\bbC\\,|\\, \\Re(z) \\in [0,1]\\}, $$ under various hypotheses on the linear operators $S$ and $T_j$, $j=1,2$. We particularly single out the case of self-adjoint and sectorial operators $T_j$ in some separable complex Hilbert space $\\cH_j$, $j=1,2$, and suppose that $S$ (resp., $S^*$) is a densely defined closed operator mapping $\\dom(S) \\subseteq \\cH_1$ into $\\cH_2$ (resp., $\\dom(S^*) \\subseteq \\cH_2$ into $\\cH_1$), relatively bounded with respect to $T_1$ (resp., $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1517","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":"1405.1517","created_at":"2026-05-18T02:52:24.624006+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.1517v1","created_at":"2026-05-18T02:52:24.624006+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1517","created_at":"2026-05-18T02:52:24.624006+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJANAECRSTWO","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJANAECRSTWO7KRK","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJANAECR","created_at":"2026-05-18T12:28:30.664211+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/GJANAECRSTWO7KRKSVCXACATNE","json":"https://pith.science/pith/GJANAECRSTWO7KRKSVCXACATNE.json","graph_json":"https://pith.science/api/pith-number/GJANAECRSTWO7KRKSVCXACATNE/graph.json","events_json":"https://pith.science/api/pith-number/GJANAECRSTWO7KRKSVCXACATNE/events.json","paper":"https://pith.science/paper/GJANAECR"},"agent_actions":{"view_html":"https://pith.science/pith/GJANAECRSTWO7KRKSVCXACATNE","download_json":"https://pith.science/pith/GJANAECRSTWO7KRKSVCXACATNE.json","view_paper":"https://pith.science/paper/GJANAECR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.1517&json=true","fetch_graph":"https://pith.science/api/pith-number/GJANAECRSTWO7KRKSVCXACATNE/graph.json","fetch_events":"https://pith.science/api/pith-number/GJANAECRSTWO7KRKSVCXACATNE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJANAECRSTWO7KRKSVCXACATNE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJANAECRSTWO7KRKSVCXACATNE/action/storage_attestation","attest_author":"https://pith.science/pith/GJANAECRSTWO7KRKSVCXACATNE/action/author_attestation","sign_citation":"https://pith.science/pith/GJANAECRSTWO7KRKSVCXACATNE/action/citation_signature","submit_replication":"https://pith.science/pith/GJANAECRSTWO7KRKSVCXACATNE/action/replication_record"}},"created_at":"2026-05-18T02:52:24.624006+00:00","updated_at":"2026-05-18T02:52:24.624006+00:00"}