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More precisely, let $2\\!<\\!q\\!<\\!\\infty$ and $T:\\,C(K)\\,\\to\\,F$ a linear, continous operator.\n  T is of gaussian cotype q if and only if\n  ( \\summ_1^n (\\frac{|| Tx_k||_F}{\\sqrt{\\log(k+1)}})^q )^{1/q} \\, \\le c || \\summ_1^n \\varepsilon_k x_k ||_{L_2(C(K))} ,\n  for all sequences with $(|| Tx_k ||)_1^n$ decreasing.\n  T is of Rademacher cotype q if and only if\n  (\\summ_1^n (|| Tx_k||_F \\,\\sqrt{\\log(k+1)})^q )^{1/q} \\, \\le c || \\summ_1^n g_k x_k ||_{L_2(C(K))} ,\n  for all "},"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":"math/9302206","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1993-02-04T19:45:37Z","cross_cats_sorted":[],"title_canon_sha256":"a4fb32d4783d4406a7e01e8a06abeef63d1b9ddc006ada815ff601d741ebf1fa","abstract_canon_sha256":"e1e5f2d6315c823fa26e70dc9fa1ab74aed527c7fa08826629b30fe8ac06756b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:52.343606Z","signature_b64":"J1HN5Gdz2VtfiH99MclRL5dE8U+jShS5H2W5hV4zmk9qsR05CcJMHwEznCn3RBa9A8LO3BIdGjtXcGbv5q+UDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15dee478e27c057d53c3b9027f3cdb248039787f693579b907a521f8f249cc1c","last_reissued_at":"2026-05-18T01:05:52.343080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:52.343080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparing gaussian and Rademacher cotype for operators on the space of continous functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marius Junge","submitted_at":"1993-02-04T19:45:37Z","abstract_excerpt":"We will prove an abstract comparision principle which translates gaussian cotype in Rademacher cotype conditions and vice versa. More precisely, let $2\\!<\\!q\\!<\\!\\infty$ and $T:\\,C(K)\\,\\to\\,F$ a linear, continous operator.\n  T is of gaussian cotype q if and only if\n  ( \\summ_1^n (\\frac{|| Tx_k||_F}{\\sqrt{\\log(k+1)}})^q )^{1/q} \\, \\le c || \\summ_1^n \\varepsilon_k x_k ||_{L_2(C(K))} ,\n  for all sequences with $(|| Tx_k ||)_1^n$ decreasing.\n  T is of Rademacher cotype q if and only if\n  (\\summ_1^n (|| Tx_k||_F \\,\\sqrt{\\log(k+1)})^q )^{1/q} \\, \\le c || \\summ_1^n g_k x_k ||_{L_2(C(K))} ,\n  for all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9302206","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":"math/9302206","created_at":"2026-05-18T01:05:52.343143+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9302206v1","created_at":"2026-05-18T01:05:52.343143+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9302206","created_at":"2026-05-18T01:05:52.343143+00:00"},{"alias_kind":"pith_short_12","alias_value":"CXPOI6HCPQCX","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"CXPOI6HCPQCX2U6D","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"CXPOI6HC","created_at":"2026-05-18T12:25:47.102015+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/CXPOI6HCPQCX2U6DXEBH6PG3ES","json":"https://pith.science/pith/CXPOI6HCPQCX2U6DXEBH6PG3ES.json","graph_json":"https://pith.science/api/pith-number/CXPOI6HCPQCX2U6DXEBH6PG3ES/graph.json","events_json":"https://pith.science/api/pith-number/CXPOI6HCPQCX2U6DXEBH6PG3ES/events.json","paper":"https://pith.science/paper/CXPOI6HC"},"agent_actions":{"view_html":"https://pith.science/pith/CXPOI6HCPQCX2U6DXEBH6PG3ES","download_json":"https://pith.science/pith/CXPOI6HCPQCX2U6DXEBH6PG3ES.json","view_paper":"https://pith.science/paper/CXPOI6HC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9302206&json=true","fetch_graph":"https://pith.science/api/pith-number/CXPOI6HCPQCX2U6DXEBH6PG3ES/graph.json","fetch_events":"https://pith.science/api/pith-number/CXPOI6HCPQCX2U6DXEBH6PG3ES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CXPOI6HCPQCX2U6DXEBH6PG3ES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CXPOI6HCPQCX2U6DXEBH6PG3ES/action/storage_attestation","attest_author":"https://pith.science/pith/CXPOI6HCPQCX2U6DXEBH6PG3ES/action/author_attestation","sign_citation":"https://pith.science/pith/CXPOI6HCPQCX2U6DXEBH6PG3ES/action/citation_signature","submit_replication":"https://pith.science/pith/CXPOI6HCPQCX2U6DXEBH6PG3ES/action/replication_record"}},"created_at":"2026-05-18T01:05:52.343143+00:00","updated_at":"2026-05-18T01:05:52.343143+00:00"}