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Moreover, there is a projection $P:Lp(M) --> Lp(M)$ onto E with $\\norm{P}_{cb} \\leq c_p n^{\\abs{1/2-1/p}}.$ We follow the classical change of density argument with appropriate noncommutative variations in addition to the opposite trick."},"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":"0711.1208","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2007-11-08T06:39:05Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"b222cef4a58165ca4de4eb4cf3e3b94289cde55b5f27af46abf8da7ca85ba204","abstract_canon_sha256":"44a84c7e8716fb30ce4f97ff5db6205025249b8f03ad38d32bc695d334a0b0ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:34.657041Z","signature_b64":"QQn936RbU+fXkr68J+47mlu62jeKLYsamJFNCBpwoVI7NaOiuTpcbT0YcPy+8D/PCq82C9wSxvdPkatIqAmVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9203ad0ed4cd89a3397abb9825b44f6963a17c7fe238866d3521c4ea7120f795","last_reissued_at":"2026-05-18T03:48:34.656525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:34.656525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite dimensional subspaces of noncommutative $L_p$ spaces","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Hun Hee Lee","submitted_at":"2007-11-08T06:39:05Z","abstract_excerpt":"We prove the following noncommutative version of Lewis's classical result. Every n-dimensional subspace E of Lp(M) (1<p<\\infty) for a von Neumann algebra M satisfies d_{cb}(E, RC^n_{p'}) \\leq c_p n^{\\abs{1/2-1/p}} for some constant c_p depending only on $p$, where $1/p +1/p' =1$ and $RC^n_{p'} = [R_n\\cap C_n, R_n+C_n]_{1/p'}$. Moreover, there is a projection $P:Lp(M) --> Lp(M)$ onto E with $\\norm{P}_{cb} \\leq c_p n^{\\abs{1/2-1/p}}.$ We follow the classical change of density argument with appropriate noncommutative variations in addition to the opposite trick."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.1208","kind":"arxiv","version":2},"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":"0711.1208","created_at":"2026-05-18T03:48:34.656593+00:00"},{"alias_kind":"arxiv_version","alias_value":"0711.1208v2","created_at":"2026-05-18T03:48:34.656593+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.1208","created_at":"2026-05-18T03:48:34.656593+00:00"},{"alias_kind":"pith_short_12","alias_value":"SIB22DWUZWE2","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"SIB22DWUZWE2GOL2","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"SIB22DWU","created_at":"2026-05-18T12:25:56.245647+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/SIB22DWUZWE2GOL2XOMCLNCPNF","json":"https://pith.science/pith/SIB22DWUZWE2GOL2XOMCLNCPNF.json","graph_json":"https://pith.science/api/pith-number/SIB22DWUZWE2GOL2XOMCLNCPNF/graph.json","events_json":"https://pith.science/api/pith-number/SIB22DWUZWE2GOL2XOMCLNCPNF/events.json","paper":"https://pith.science/paper/SIB22DWU"},"agent_actions":{"view_html":"https://pith.science/pith/SIB22DWUZWE2GOL2XOMCLNCPNF","download_json":"https://pith.science/pith/SIB22DWUZWE2GOL2XOMCLNCPNF.json","view_paper":"https://pith.science/paper/SIB22DWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0711.1208&json=true","fetch_graph":"https://pith.science/api/pith-number/SIB22DWUZWE2GOL2XOMCLNCPNF/graph.json","fetch_events":"https://pith.science/api/pith-number/SIB22DWUZWE2GOL2XOMCLNCPNF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SIB22DWUZWE2GOL2XOMCLNCPNF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SIB22DWUZWE2GOL2XOMCLNCPNF/action/storage_attestation","attest_author":"https://pith.science/pith/SIB22DWUZWE2GOL2XOMCLNCPNF/action/author_attestation","sign_citation":"https://pith.science/pith/SIB22DWUZWE2GOL2XOMCLNCPNF/action/citation_signature","submit_replication":"https://pith.science/pith/SIB22DWUZWE2GOL2XOMCLNCPNF/action/replication_record"}},"created_at":"2026-05-18T03:48:34.656593+00:00","updated_at":"2026-05-18T03:48:34.656593+00:00"}