{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MNV4AH2H4BPJLZTGNR55BP3HMX","short_pith_number":"pith:MNV4AH2H","schema_version":"1.0","canonical_sha256":"636bc01f47e05e95e6666c7bd0bf6765f727069586cd449b87f9810506ac79f4","source":{"kind":"arxiv","id":"1112.1302","version":1},"attestation_state":"computed","paper":{"title":"Fuglede-Putnam type theorems via the Aluthge transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"M. S. Moslehian, S. M. S. Nabavi Sales","submitted_at":"2011-12-06T15:06:08Z","abstract_excerpt":"Let $A=U|A|$ and $B=V|B|$ be the polar decompositions of $A\\in \\mathbb{B}(\\mathscr{H}_1)$ and $B\\in \\mathbb{B}(\\mathscr{H}_2)$ and let $Com(A,B)$ stand for the set of operators $X\\in\\mathbb{B}(\\mathscr{H}_2,\\mathscr{H}_1)$ such that $AX=XB$. A pair $(A,B)$ is said to have the FP-property if $Com(A,B)\\subseteqCom(A^\\ast,B^\\ast)$. Let $\\tilde{C}$ denote the Aluthge transform of a bounded linear operator $C$. We show that (i) if $A$ and $B$ are invertible and $(A,B)$ has the FP-property, then so is $(\\tilde{A},\\tilde{B})$; (ii) if $A$ and $B$ are invertible, the spectrums of both $U$ and $V$ are "},"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":"1112.1302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-06T15:06:08Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"dbebcfb57b976a4c6172c7574e31d923fd62fb3776a7a6a85370d37ea76e7e35","abstract_canon_sha256":"19a133ff18f1f486ef19692dda0f8081514ab9cc426d174d5eedffcec0e32751"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:27.798472Z","signature_b64":"djrGrxReftXsRPP4wj/TwIzv0eLFgOU1Qc9KV/Oqccg7mpr1x1oWYjFYOlQFZ9rSG8rdpQTxKth6CENzfQ4jBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"636bc01f47e05e95e6666c7bd0bf6765f727069586cd449b87f9810506ac79f4","last_reissued_at":"2026-05-18T03:29:27.797752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:27.797752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fuglede-Putnam type theorems via the Aluthge transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"M. S. Moslehian, S. M. S. Nabavi Sales","submitted_at":"2011-12-06T15:06:08Z","abstract_excerpt":"Let $A=U|A|$ and $B=V|B|$ be the polar decompositions of $A\\in \\mathbb{B}(\\mathscr{H}_1)$ and $B\\in \\mathbb{B}(\\mathscr{H}_2)$ and let $Com(A,B)$ stand for the set of operators $X\\in\\mathbb{B}(\\mathscr{H}_2,\\mathscr{H}_1)$ such that $AX=XB$. A pair $(A,B)$ is said to have the FP-property if $Com(A,B)\\subseteqCom(A^\\ast,B^\\ast)$. Let $\\tilde{C}$ denote the Aluthge transform of a bounded linear operator $C$. We show that (i) if $A$ and $B$ are invertible and $(A,B)$ has the FP-property, then so is $(\\tilde{A},\\tilde{B})$; (ii) if $A$ and $B$ are invertible, the spectrums of both $U$ and $V$ are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1302","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":"1112.1302","created_at":"2026-05-18T03:29:27.797882+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.1302v1","created_at":"2026-05-18T03:29:27.797882+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1302","created_at":"2026-05-18T03:29:27.797882+00:00"},{"alias_kind":"pith_short_12","alias_value":"MNV4AH2H4BPJ","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"MNV4AH2H4BPJLZTG","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"MNV4AH2H","created_at":"2026-05-18T12:26:34.985390+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/MNV4AH2H4BPJLZTGNR55BP3HMX","json":"https://pith.science/pith/MNV4AH2H4BPJLZTGNR55BP3HMX.json","graph_json":"https://pith.science/api/pith-number/MNV4AH2H4BPJLZTGNR55BP3HMX/graph.json","events_json":"https://pith.science/api/pith-number/MNV4AH2H4BPJLZTGNR55BP3HMX/events.json","paper":"https://pith.science/paper/MNV4AH2H"},"agent_actions":{"view_html":"https://pith.science/pith/MNV4AH2H4BPJLZTGNR55BP3HMX","download_json":"https://pith.science/pith/MNV4AH2H4BPJLZTGNR55BP3HMX.json","view_paper":"https://pith.science/paper/MNV4AH2H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.1302&json=true","fetch_graph":"https://pith.science/api/pith-number/MNV4AH2H4BPJLZTGNR55BP3HMX/graph.json","fetch_events":"https://pith.science/api/pith-number/MNV4AH2H4BPJLZTGNR55BP3HMX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MNV4AH2H4BPJLZTGNR55BP3HMX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MNV4AH2H4BPJLZTGNR55BP3HMX/action/storage_attestation","attest_author":"https://pith.science/pith/MNV4AH2H4BPJLZTGNR55BP3HMX/action/author_attestation","sign_citation":"https://pith.science/pith/MNV4AH2H4BPJLZTGNR55BP3HMX/action/citation_signature","submit_replication":"https://pith.science/pith/MNV4AH2H4BPJLZTGNR55BP3HMX/action/replication_record"}},"created_at":"2026-05-18T03:29:27.797882+00:00","updated_at":"2026-05-18T03:29:27.797882+00:00"}