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Junge","submitted_at":"2017-04-08T02:21:23Z","abstract_excerpt":"Let $\\mathcal{L}(H)$ be the $*$-algebra of all bounded operators on an infinite dimensional Hilbert space $H$ and let $(\\mathcal{I}, \\|\\cdot\\|_{\\mathcal{I}})$ be an ideal in $\\mathcal{L}(H)$ equipped with a Banach norm which is distinct from the Schatten-von Neumann ideal $\\mathcal{L}_p(\\mathcal{H})$, $1\\leq p<2$. We prove that $\\mathcal{I}$ isomorphically embeds into an $L_p$-space $\\mathcal{L}_p(\\mathcal{R}),$ $1\\leq p<2,$ (here, $\\mathcal{R}$ is the hyperfinite II$_1$-factor) if its commutative core (that is, Calkin space for $\\mathcal{I}$) isomorphically embeds into $L_p(0,1).$ Furthermore"},"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":"1704.02423","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2017-04-08T02:21:23Z","cross_cats_sorted":[],"title_canon_sha256":"ce751993f8a1763fb9367aac8c2574cba515f34c0179b3b8e02bca8d30e89975","abstract_canon_sha256":"4d5dd75f412d95259114d5ca65fffeabd0f3e6f1334966a2766e56b1e9e7b51f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:45.597193Z","signature_b64":"hk6KvALVlK8M+x83PqojiDOxVooNZSXhqDmrFacdtXNDslHmb8BkZLjqOKT5Tbi1vOD/NlV8ms4Npi4DYDrbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0a7deea7a7d33bf4f6084e04f235e3732ace071ea88f71b6fca7d3558ae1f04","last_reissued_at":"2026-05-18T00:46:45.596405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:45.596405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embeddings of operator ideals into $\\mathcal{L}_p-$spaces on finite von Neumann algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"D. Zanin, F. Sukochev, M. Junge","submitted_at":"2017-04-08T02:21:23Z","abstract_excerpt":"Let $\\mathcal{L}(H)$ be the $*$-algebra of all bounded operators on an infinite dimensional Hilbert space $H$ and let $(\\mathcal{I}, \\|\\cdot\\|_{\\mathcal{I}})$ be an ideal in $\\mathcal{L}(H)$ equipped with a Banach norm which is distinct from the Schatten-von Neumann ideal $\\mathcal{L}_p(\\mathcal{H})$, $1\\leq p<2$. We prove that $\\mathcal{I}$ isomorphically embeds into an $L_p$-space $\\mathcal{L}_p(\\mathcal{R}),$ $1\\leq p<2,$ (here, $\\mathcal{R}$ is the hyperfinite II$_1$-factor) if its commutative core (that is, Calkin space for $\\mathcal{I}$) isomorphically embeds into $L_p(0,1).$ Furthermore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02423","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":"1704.02423","created_at":"2026-05-18T00:46:45.596676+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.02423v1","created_at":"2026-05-18T00:46:45.596676+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02423","created_at":"2026-05-18T00:46:45.596676+00:00"},{"alias_kind":"pith_short_12","alias_value":"2CT552T2PUZ3","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2CT552T2PUZ36T3A","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2CT552T2","created_at":"2026-05-18T12:30:55.937587+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/2CT552T2PUZ36T3AQTQE6I26G4","json":"https://pith.science/pith/2CT552T2PUZ36T3AQTQE6I26G4.json","graph_json":"https://pith.science/api/pith-number/2CT552T2PUZ36T3AQTQE6I26G4/graph.json","events_json":"https://pith.science/api/pith-number/2CT552T2PUZ36T3AQTQE6I26G4/events.json","paper":"https://pith.science/paper/2CT552T2"},"agent_actions":{"view_html":"https://pith.science/pith/2CT552T2PUZ36T3AQTQE6I26G4","download_json":"https://pith.science/pith/2CT552T2PUZ36T3AQTQE6I26G4.json","view_paper":"https://pith.science/paper/2CT552T2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.02423&json=true","fetch_graph":"https://pith.science/api/pith-number/2CT552T2PUZ36T3AQTQE6I26G4/graph.json","fetch_events":"https://pith.science/api/pith-number/2CT552T2PUZ36T3AQTQE6I26G4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2CT552T2PUZ36T3AQTQE6I26G4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2CT552T2PUZ36T3AQTQE6I26G4/action/storage_attestation","attest_author":"https://pith.science/pith/2CT552T2PUZ36T3AQTQE6I26G4/action/author_attestation","sign_citation":"https://pith.science/pith/2CT552T2PUZ36T3AQTQE6I26G4/action/citation_signature","submit_replication":"https://pith.science/pith/2CT552T2PUZ36T3AQTQE6I26G4/action/replication_record"}},"created_at":"2026-05-18T00:46:45.596676+00:00","updated_at":"2026-05-18T00:46:45.596676+00:00"}