{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PGV6WAWPEXV3JXF7VWJ66V4KB5","short_pith_number":"pith:PGV6WAWP","schema_version":"1.0","canonical_sha256":"79abeb02cf25ebb4dcbfad93ef578a0f6f1c1bda59063f255c25c3c9b7edb6ed","source":{"kind":"arxiv","id":"1907.07147","version":1},"attestation_state":"computed","paper":{"title":"Skew-Hermitian operators in real Banach spaces of self-adjoint compact operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B. Aminov, Vladimir Chilin","submitted_at":"2019-07-15T02:47:23Z","abstract_excerpt":"Let $\\mathcal H$ be a complex infinite-dimensional separable Hilbert space, and let $\\mathcal K(\\mathcal H)$ be the $C^*$-algebra of compact linear operators in $\\mathcal H$. Let $(E,\\|\\cdot\\|_E)$ be a symmetric sequence space. If $\\{\\mu(n,x)\\}$ are the singular values of $x\\in\\mathcal K(\\mathcal H)$, let $\\mathcal C_E=\\{x\\in\\mathcal K(\\mathcal H): \\{\\mu(n,x)\\}\\in E\\}$ with $\\|x\\|_{\\mathcal C_E}=\\|\\{\\mu(n,x)\\}\\|_E$, $x\\in\\mathcal C_E$, be the Banach ideal of compact operators generated by $E$. Let $\\mathcal C_E^h=\\{x\\in\\mathcal C_E : x=x^*\\}$ be the real Banach subspace of self-adjoint operato"},"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":"1907.07147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-15T02:47:23Z","cross_cats_sorted":[],"title_canon_sha256":"74b456ac27e87e819c5be53073615dee5a35447f31cc2dbc4e5ff4319dc1e91d","abstract_canon_sha256":"5ca2290937f7e3c6bc291a1d562c140f2f55feb8c135ad942175fc837f70e04a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:27.875595Z","signature_b64":"ka2dEWLBJgzysugjoU9CQFkzoAXrKLaCqfkMMruM31l5SITrP0JHJbNsZLKafLxvp1NIJn6w9bUPKHjORd/JAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79abeb02cf25ebb4dcbfad93ef578a0f6f1c1bda59063f255c25c3c9b7edb6ed","last_reissued_at":"2026-05-17T23:40:27.874825Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:27.874825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Skew-Hermitian operators in real Banach spaces of self-adjoint compact operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B. Aminov, Vladimir Chilin","submitted_at":"2019-07-15T02:47:23Z","abstract_excerpt":"Let $\\mathcal H$ be a complex infinite-dimensional separable Hilbert space, and let $\\mathcal K(\\mathcal H)$ be the $C^*$-algebra of compact linear operators in $\\mathcal H$. Let $(E,\\|\\cdot\\|_E)$ be a symmetric sequence space. If $\\{\\mu(n,x)\\}$ are the singular values of $x\\in\\mathcal K(\\mathcal H)$, let $\\mathcal C_E=\\{x\\in\\mathcal K(\\mathcal H): \\{\\mu(n,x)\\}\\in E\\}$ with $\\|x\\|_{\\mathcal C_E}=\\|\\{\\mu(n,x)\\}\\|_E$, $x\\in\\mathcal C_E$, be the Banach ideal of compact operators generated by $E$. Let $\\mathcal C_E^h=\\{x\\in\\mathcal C_E : x=x^*\\}$ be the real Banach subspace of self-adjoint operato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07147","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":"1907.07147","created_at":"2026-05-17T23:40:27.874955+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.07147v1","created_at":"2026-05-17T23:40:27.874955+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07147","created_at":"2026-05-17T23:40:27.874955+00:00"},{"alias_kind":"pith_short_12","alias_value":"PGV6WAWPEXV3","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"PGV6WAWPEXV3JXF7","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"PGV6WAWP","created_at":"2026-05-18T12:33:24.271573+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/PGV6WAWPEXV3JXF7VWJ66V4KB5","json":"https://pith.science/pith/PGV6WAWPEXV3JXF7VWJ66V4KB5.json","graph_json":"https://pith.science/api/pith-number/PGV6WAWPEXV3JXF7VWJ66V4KB5/graph.json","events_json":"https://pith.science/api/pith-number/PGV6WAWPEXV3JXF7VWJ66V4KB5/events.json","paper":"https://pith.science/paper/PGV6WAWP"},"agent_actions":{"view_html":"https://pith.science/pith/PGV6WAWPEXV3JXF7VWJ66V4KB5","download_json":"https://pith.science/pith/PGV6WAWPEXV3JXF7VWJ66V4KB5.json","view_paper":"https://pith.science/paper/PGV6WAWP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.07147&json=true","fetch_graph":"https://pith.science/api/pith-number/PGV6WAWPEXV3JXF7VWJ66V4KB5/graph.json","fetch_events":"https://pith.science/api/pith-number/PGV6WAWPEXV3JXF7VWJ66V4KB5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PGV6WAWPEXV3JXF7VWJ66V4KB5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PGV6WAWPEXV3JXF7VWJ66V4KB5/action/storage_attestation","attest_author":"https://pith.science/pith/PGV6WAWPEXV3JXF7VWJ66V4KB5/action/author_attestation","sign_citation":"https://pith.science/pith/PGV6WAWPEXV3JXF7VWJ66V4KB5/action/citation_signature","submit_replication":"https://pith.science/pith/PGV6WAWPEXV3JXF7VWJ66V4KB5/action/replication_record"}},"created_at":"2026-05-17T23:40:27.874955+00:00","updated_at":"2026-05-17T23:40:27.874955+00:00"}